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Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) resolution of cusp singularities; Shintani decomposition; totally real cubic number fields; Hilbert modular variety; family of cubics; evaluation of zeta-function DOI: 10.1007/BF01359864 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) formally real fields; valuation theory; Waring problems; Krull valuation; real holomorphy ring; totally-positive units; sums of \(2n\)-th powers; totally Archimedean; Pythagoras number; Pythagorean number field; fan; strictly Pythagorean Eberhard Becker, The real holomorphy ring and sums of 2\?th powers, Real algebraic geometry and quadratic forms (Rennes, 1981) Lecture Notes in Math., vol. 959, Springer, Berlin-New York, 1982, pp. 139 -- 181. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's 16-th problem; types of real algebraic varieties; hyperboloid V. I. Zvonilov, ''Stratified spaces of real algebraic curves of bidegree (m, 1) and (m, 2) on a hyperboloid,''Amer. Math. Soc. Transl. Ser. 2,173, 253--264 (1996). | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's sixteenth problem; real algebraic curves; isotopy of algebraic hypersurface | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real algebraic plane curve; Hilbert 16th problem; singularities of plane curve; constructing curves of a given degree; prescribed arrangement; perturbing singular curves with controlled variation of the topology; Ragdale's conjecture Brugallé, E.: Tropical curves, notes from introductary lectures given in July 2013 at Max Planck Institute for Mathematics, Bonn. http://erwan.brugalle.perso.math.cnrs.fr/articles/TropicalBonn/TropicalCurves | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) semialgebraic sets; quantifier elimination; theory of real closed fields; exponential space; NC circuit M. Ben-Or, D. Kozen and J. Reif, ''The complexity of elementary algebra and geometry,''Journal of Computer and System Sciences 32 (1986) 251--264. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real algebraic geometry; semidefinite programming; sums of squares decomposition; Reznick's representation; Putinar's representation; hybrid numeric-symbolic algorithm | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) local rings; completion; Artin approximation; preorderings; curve singularities; positive polynomials; sums of squares; real algebraic geometry; henselian ring; excellent ring; Krull topology; saturation; nonnegativity certificate; real spectrum; constructible topology; spectral topology; basic semialgebraic sets; local global principles C. Scheiderer, \textit{Weighted sums of squares in local rings and their completions}, I. Math. Z., 266 (2010), pp. 1--19. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) 17th problem of Hilbert; Kochen operator; p-adically closed fields; isomorphism theorem; general embedding theorem; Hilbert Nullstellensatz Prestel, A., Roquette, P.: Formally \(p\)-adic Fields, volume 1050 of Lecture Notes in Mathematics. Springer, Berlin (1984) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real algebraic variety; Hilbert's 16th problem; topology of real algebraic curves; curves on ellipsoid | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) lifting problem; deformation of \({\mathbb{G}}_ a\) to \({\mathbb{G}}_ m\); characteristic p; automorphism group; Galois covering of curves; class field theory; Artin-Schreier sequence; Kummer sequence Sekiguchi, T.; Oort, F.; Suwa, N., On the deformation of Artin-Schreier to Kummer, Annales Scientifiques de l'École Normale Supérieure, 22, 345-375, (1989) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) isotropy; local-global principle; real field; sums of squares; \(u\)-invariant; pythagoras number; valuation; algebraic function fields Becher, Karim; Grimm, David; Van Geel, Jan: Sums of squares in algebraic function fields over a complete discretely valued field, Pacific J. Math. 267, No. 2, 257-276 (2014) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Viro's method of constructing real algebraic hypersurfaces; Hilbert's 16th problem J.-J. Risler, Construction d'hypersurfaces réelles (d'après Viro) , Astérisque 216 (1993), 69--86., Séminaire Bourbaki 1992/93, exp. no. 763. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) 17th problem of Hilbert; Kochen operator; p-adically closed fields; isomorphism theorem; general embedding theorem; zero theorem of Hilbert Prestel, A.: Lectures on formally real fields. Lecture notes in mathematics 1093 (1983) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) piecewise-polynomial functions; sup-inf-polynomially definable functions; almost \(f\)-rings; real closed field; Hilbert's 17th problem; continuous PWP functions; Stengle's Nichtnegativstellensatz; Stellensätze; SIPD functions; real spectrum | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) descent; Hilbert's irreducibility theorem; Galois coverings; inverse problem of Galois theory; Hilbertian field D. Harbater, ''Galois coverings of the arithmetic line,'' in Number Theory, New York: Springer-Verlag, 1987, pp. 165-195. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) \(p\)-extensions of algebraic function fields; Artin-Schreier theory; characteristic \(p\); genus; number of rational points; coding theory; gap number Arnaldo Garcia and Henning Stichtenoth, Elementary abelian \(p\)-extensions of algebraic function fields, Manuscr. Math. 72 (1991), 67--79. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Polya's representation; Putinar's representation; hybrid numeric-symbolic algorithm; real algebraic geometry; semidefinite programming; sums of squares decomposition | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) algebraic number fields; valuation theory; class field theory; Arakelov theory; zeta functions; \(L\)-series; algebraic curves over arithmetic ground fields; arithmetic algebraic geometry; geometric approach to algebraic orders; singular algebraic curves; Grothendieck-Riemann-Roch theory for algebraic schemes; Hecke's \(L\)-series; Artin theory of \(L\)-series; selected exercises Neukirch, Jürgen, Algebraische zahlentheorie, (1992), Springer-Verlag Berlin, (in German) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real closed fields; finite \(K\)-algebra; Hermitian forms; quadratic forms; Sylvester's law of inertia; type; signature; trace forms | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real algebraic surfaces; Hilbert's 16-th problem; complexification; mutual positions of connected components of a nonsingular plane real algebraic curve of given degree O. Ya Viro, Progress in the topology of real algebraic varieties over the last six years, \textit{Uspekhi Mat. Nauk.}\textbf{41} (1986) 45-67 (in Russian); \textit{Russian Math. Surveys}\textbf{41} (1986) 55-82. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) algebraic curves; real algebraic geometry; projective curves; conic sections; celestial mechanics; Hilbert's 16th problem; topology of algebraic curves; Riemann surfaces | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's 16th problem; Viro's method; \(T\)-curve; depth of nests; real algebraic scheme J. A. de Loera and F. J. Wicklin,On the need of convexity in patchworking, Advances in Applied Mathematics20 (1998), 188--219. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) positive-definite germ of an analytic function; sum of squares; Hilbert's 17th problem; singular points of a germ of a function | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Towers of function fields; congruence function fields; genus; rational places; limits of towers; Zink's bound; cubic finite fields; Artin--Schreier extensions; Drinfeld--Vlăduţ bound; Hasse--Weil bound [4]A. Bassa, A. Garcia and H. Stichtenoth, A new tower over cubic finite fields, Moscow Math. J. 8 (2008), 401--418. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) differential ring; ordered differential field; differential inequalities; real differential spectrum; Hilbert's 17th problem; Hörmander- Łojasiewicz inequality Stengle, G., Algebraic theory of differential inequalities, Comm. Algebra, 19, 6, 1743-1763, (1991) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) rational functions; meromorphic functions; real algebraic sets; function fields; real algebraic geometry; Hilbert's \(17^{th}\); problem; orderings; analytic germ | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) \(f\)-rings; rings of semi-algebraic functions; rings of piecewise polynomial functions; rings of sup-inf-definable functions; real algebra; Stellensätze; Hilbert's 17th problem DelMad1995 Charles N. Delzell and James J. Madden, \emph Lattice-ordered rings and semialgebraic geometry. I, Real analytic and algebraic geometry (Trento, 1992), de Gruyter, Berlin, 1995, pp.~103--129. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) positive definite germ of an analytic function; sum of squares; Hilbert's 17th problem; singular points of a germ of a function Jaworski, P.: About estimates on number of squares necessary to represent a positive-semidefinite analytic function. Arch. math. 58, 276-279 (1992) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Schmuedgen's representation theorem; quadratic forms; sums of squares; Henselization; Witt's Local Global Principle; algebraic curves; archimedian quadratic module; valuation theory; effectivity in semialgebraic geometry | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) finite fields; number theory; algebraic geometry; permutation polynomials; multilinear equations; quadratic forms; characters; Gauss sums; Jacobi sums; diagonal equations; zeta function; Chevalley's theorem; law of quadratic reciprocity; Davenport-Hasse theorem; Fermat curve; elliptic curve Small, C.: Arithmetic of finite fields. Monogr. textbooks pure appl. Math. 148 (1991) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) elliptic curves; Hilbert's tenth problem; real fields; \(p\)-adic fields Moret-Bailly, Laurent, Elliptic curves and Hilbert's tenth problem for algebraic function fields over real and \textit{p}-adic fields, J. Reine Angew. Math., 587, 77-143, (2006) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) \(M\)-curves; Newton polygon; smoothing of singular points; Hilbert's 16th problem; oval arrangements of real plane nonsingular curves of degree 9 A. B. Korchagin, Construction of new \?-curves of 9th degree, Real algebraic geometry (Rennes, 1991) Lecture Notes in Math., vol. 1524, Springer, Berlin, 1992, pp. 296 -- 307. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) mixed Taylor formulas; formally real field; Hilbert Nullstellensatz; Positiv-Stellensatz; constructive proof of the real nullstellensatz; ordered field; Hörmander algorithm Lombardi, H.: Théorème effectif des zéros réel et variantes. Publications mathématiques de besançon 1 (1988--1989) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) natural Lagrangian system; monoidal transformation of real analytic manifold; normal crossing; logarithmic fields; inversion of Lagrange-Dirichlet theorem; critical point; analytic potential function; Lyapunov's problem; supercritical motions; Lagrangian system with gyroscopic forces Palamodov, V.P.: Stability of motion and algebraic geometry. In: Dynamical Systems in Classical Mechanics (Amer. Math. Soc. Transl. Ser. 2), vol. 168, 5--20 (1995) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) subexponential-time algorithm; connected components of a semialgebraic set; first-order theory of real closed fields; exponential time | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) linear algebraic group acting rationally on an algebra; fundamental problem of invariant theory; Hilbert's fourteenth problem Hochster, M.: The invariant theory of commutative rings. Contemp. math. 43, 161-179 (1985) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) fast algorithm; number of connected components; semialgebraic set; first order theory of real closed fields | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real algebraic curve; Hilbert's 16th problem; smoothing of singularities; isotopy classification; real loci of non-singular algebraic curves of degeee 8 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) positive polynomial; sum of squares of rational functions; Hilbert's 17th problem; noncommutative polynomials Helton, JW, ''positive'' non-commutative polynomials are sums of squares, Ann. Math., 156, 675-694, (2002) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's 16th problem; Seifert form of a link; Murasugi-Tristram inequality; quasipositive braids; topology of real plane algebraic curves; M-curves; degree; complex orientations Schuh, F.: An equation of reality for real and imaginary plane curves with higher singularities. Proc. Sect. Sci. R. Acad. Amst. \textbf{6}, 764-773, 1903-1904 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert modular varieties; descent obstruction; Galois representations; Serre's conjecture; abelian varieties of \(\mathrm{GL}_2\)-type; totally real fields | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Towers of function fields; congruence function fields; genus; rational places; limits of towers; Zink's bound; cubic finite fields; Artin--Schreier extensions; Drinfeld--Vlăduţ bound; Hasse--Weil bound. Bezerra, J.; Garcia, A.; Stichtenoth, H.: An explicit tower of function fields over cubic finite fields and Zink's lower bound for \(A(q3)\). J. reine angew. Math. 589, 159-199 (2005) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) subexponential-time algorithm; connected components of a semialgebraic set; first-order theory of real closed fields; exponential time | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) positive polynomials; sums of squares; real algebraic geometry; moment problem; weighted norm topologies Marshall, M.: Positive polynomials and sums of squares, Mathematical Surveys and Monographs \textbf{146}. Amer. Math. Soc., Providence, RI (2008) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Galois covers; lifting of automorphisms of curves; \(p\)-adic discs; curves over local fields; characteristic \(p\); Witt vectors; Kummer-Artin-Schreier-Witt theory B. Green and M. Matignon, ''Liftings of Galois covers of smooth curves,'' Compositio Math., vol. 113, iss. 3, pp. 237-272, 1998. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) invariant theory; geometric invariant theory; geometric quotients; orbit spaces; Hilbert's fourteenth problem; Lie groups; GIT; configurations of linear subspaces; linearizations of actions; classification theory; stability [7] I. Dolgachev, \(Lectures on invariant theory\), Cambridge University Press, (2003). &MR 20 | &Zbl 1023. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) smooth projective varieties; flag varieties; Miyaoka's semipositivity theorem; cotangent bundle; rational surfaces; divisorial contractions; fibrations; crystalline differential operators; étale fundamental group; semistability; reflexives sheaves; semipositive sheaves; uniruled varieties; Riemann-Hilbert correspondence; stable Higgs bundle; Chern classes; flat connections; Artin's criterion of contractibility; Kodaira dimension; Hirzebruch surface; canonical divisor; surfaces of general type; Barlow's surfaces; del Pezzo surfaces; Fano three-folds | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) decidability; Hilbert's Tenth Problem; uncomputably large integral points on algebraic curves; diophantine prefix; polynomials; height bounds; geometry of complex surfaces and 3-folds J.M. Rojas, Uncomputably large integral points on algebraic plane curves?, Theoret. Comput. Sci., 235 (this Vol.) (2000) 145--162. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) finite generation of invariant algebra; Hilbert's fourteenth problem; Popov-Pommerening conjecture Tan, L., \textit{some recent developments in the Popov-pommerening conjecture}, Group actions and invariant theory, 207-220, (1989), American Mathematical Society, Providence, RI | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) sums of units; theorem of Picard-Borel; rational points; Hilbert's irreducibility theorem; finiteness of number of holomorphic mappings; quasiprojective spaces; de Franchis theorem | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) formally real field; regularly r-closed fields; pseudo-real closed fields; ordered fields; existentially closed; axiomatizable; irreducible variety; PRC-field Basarab, Serban A.: Definite functions on algebraic varieties over ordered fields. Rev. roumaine math. Pures appl. 29, 527-535 (1984) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) balls; quotients; Shimura varieties; Hilbert's 12th problem; class fields; elliptic curves; abelian varieties; automorphic functions Rolf-Peter Holzapfel, The ball and some Hilbert problems, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 1995. Appendix I by J. Estrada Sarlabous. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) analytic germ; semi-analytic real spectrum; space of orders of the field of germs of meromorphic functions; formal half branch; maximum dimension locus; Hilbert 17th problem Ruiz, J.: Central orderings in fields of real meromorphic function germs. Preprint (1984) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) dual variety; noncompact real algebraic variety; semidefinite representations; sums of squares; theta bodies | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) rational points; hypersurface; counting function; multiple exponential sum; singular locus; Deligne's bounds for exponential sums; number of points; hypersurfaces over finite fields Heath-Brown, DR, The density of rational points on nonsingular hypersurfaces, Proc. Indian Acad. Sci. Math. Sci., 104, 13-29, (1994) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's sixteenth problem; limit cycle; Abelian and iterated integrals; bifurcation; polynomial and analytic vector fields | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real algebraic geometry; sums of squares; special curves; surfaces of minimal degree | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) bibliography; Hilbert's basis theorem; dictionary: commutative algebra-projective algebraic geometry; Hilbert's syzygy theorem; Hilbert's Nullstellensatz; Hilbert polynomials; dimension theory; Dedekind domains; Hilbert-Samuel functions; elimination theory; computer algebra; modules of differentials; homological methods; Koszul complex; Cohen-Macaulay property; duality theory; linkage Eisenbud D, \textit{Commutative Algebra: With a View Toward Algebraic Geometry}, 150, Springer New York, 1995. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) isomorphic deformation theories; deformation theory of space curves; Hilbert scheme of curves; deformation theories of a closed subscheme Charles H. Walter, Some examples of obstructed curves in \?³, Complex projective geometry (Trieste, 1989/Bergen, 1989) London Math. Soc. Lecture Note Ser., vol. 179, Cambridge Univ. Press, Cambridge, 1992, pp. 324 -- 340. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) positive semidefinite elements; sums of squares; real spectrum; singularities; excellent henselian ring; dimension 2; completion | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) invariants of finite group; inverse problem of Galois theory; Noether's problem; function field of a torus; Algebraic Tori; rational points of tori Swan, R. G.: Noether's problems in Galois theory. Symposium ''emmy Noether in bryn mawr'' (1983) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's 14-th problem; ring of invariants A'campo-Neuen, A.: Note on a counterexample to Hilbert's fourteenth problem given by P. Roberts. Indag. math. (N.S.) 5, 253-257 (1994) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) algebraic function fields; domain of regularity; Hilbert's irreducibility theorem | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Lüroth problem; intermediate Jacobians; non-closed fields; real algebraic geometry; unramified cohomology | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real plane algebraic curves; Hilbert's 16th problem Christopher, C., Polynomial Vector Fields with Prescribed Algebraic Limit Cycles, Geom. Dedicata, 2001, vol. 88, pp. 255--258. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) equations over finite fields; elliptic curves; diophantine equations in two variables; quadratic residues; large sieve; Mordell's theorem; Riemann Roch theorem; rational points; integral points; Thue equation; superelliptic equations; nonstandard arithmetic; Hilbert's tenth problem Stepanov, SA: Arithmetic of Algebraic Curves Translated from the Russian by Irene Aleksanova. Monographs in Contemporary Mathematics. Consultants Bureau, New York (1994). | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) extensions of function field; generic Galois extension; Kummer theory; Leopoldt's conjecture; cyclotomic fields; geometric class field theory C. Greither, Cyclic Galois extensions of commutative rings. Lecture Notes in Mathematics, vol. 1534. Springer, Berlin-Heidelberg-New York, 1992. Zbl0788.13003 MR1222646 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) automorphisms; curves; \(p\)-groups; Ray class fields; Artin-Schreier-Witt theory Matignon, M; Rocher, M, Smooth curves having a large automorphism p-group in characteristic p>\(0\), Algebra Number Theory, 2, 887-926, (2008) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) global function fields; Artin-Schreier extensions; genus; rational places; towers; limit of towers; asymptotically good towers | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) moduli space of curves; algebraic group actions; Hilbert's fourteenth problem; stability; toric varieties Dolgachev, I. V., Introduction to geometric invariant theory, Lecture Notes Series, vol. 25, (1994), Seoul National University, Research Institute of Mathematics, Global Analysis Research Center Seoul | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) irreducible closed semialgebraic set; orders of function fields; real algebraic sets Andradas, C.; Gamboa, J. M., On projections of real algebraic varieties, Pacific J. Math., 121, 2, 281-291, (1986) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's fourteenth problem; algebraic group; finite; generation of algebra of invariant functions Grosshans, F.D.: Hilbert's fourteenth problem for non-reductive groups. Math. Z.193, 95--103 (1986) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) transcendence; exponential function; Drinfeld module; lattice; analog of Siegel's lemma; Hilbert's 7th problem Yu, J.: Transcendence theory over function fields. Duke math. J. 52, 517-527 (1985) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) valuation rings of function fields; coordinate ring of affine; variety over a real closed field; prime cone | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) irreducible semialgebraic set; irreducible components of a semialgebraic set; Nash function; Nash set; w-Nash set; q-Nash set; substitution theorem; positivstellensätze; 17th Hilbert problem and real nullstellensatz Fernando, José F.; Gamboa, J. M., On the irreducible components of a semialgebraic set, Internat. J. Math., 23, 4, 1250031, 40 pp., (2012) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) rationality; Noether's problem; inverse Galois theory; groups of order 16 M. Kang, Noether's problem for dihedral 2-groups II, Pacific J. Math. 222 (2005), 301\ 316. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) moduli space; singular quadrics; Hilbert scheme of curves; Brill-Noether theory; Kodaira's dimension | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) polynomial inequality; real polynomial; resultant; subresultant; cylindrical algebraic decomposition; sums of squares | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Putinar's Positivstellensatz; sums of squares; degree bounds | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) sums of squares; hereditarily Pythagorean fields; hereditarily Euclidean fields; Pythagoras number; u-invariant Becher K.J., Van Geel J.: Sums of squares in function fields of hyperelliptic curves. Math. Z. 209, 829--844 (2009) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) \(M\)-surface; 16th Hilbert problem; real surfaces; maximal number of real critical points | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) division points of Drinfeld modules; arithmetic of function fields; class numbers; cyclotomic function fields; zeta-functions; Teichmüller characters; Artin conjecture; Artin L-series; p-adic measure; Main conjecture of Iwasawa theory; Frobenius; p-class groups; Bernoulli- Carlitz numbers Goss, D.: Analogies between global fields. Canad. math. Soc. conf. Proc. 7, 83-114 (1987) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Chevalley-Weil theorem; étale cover; specializations; class groups of number fields; Hilbert's irreducibility theorem | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) formally real field; orderings of higher level; signatures; survey; Kadison-Dubois theorem; real valuation rings; real holomorphy ring; Waring numbers; preordering of finite exponent; reduced Witt ring; uniqueness of real closures; model theory; absolute Galois groups; decidability; model completeness; real closed Nullstellensatz E. Becker: ?Extended Artin-Schreier theory of fields?, Rocky Mountain J. of Math., vol. 14, \# 4, Fall 1984 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Putinar's Positivstellensatz; sums of squares; quadratic module; degree bounds | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) local fields; local class field theory; Dedekind rings; different; discriminant; ramification groups; cyclotomic fields; Hasse's norm theory; cohomology of groups; Galois cohomology; Brauer group; class formation Serre, J.-P., Corps locaux, Actualités Sci. Indust., vol. 1296, (1962), Hermann | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) specialization; algebraic covers; twisting lemma; Hilbert's irreducibility theorem; Grunwald's problem; PAC fields; local fields; global fields; Hurwitz spaces Dèbes, Pierre and Legrand, François Specialization results in Galois theory Trans. Amer. Math. Soc.365 (2013) 5259--5275 Math Reviews MR3074373 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Positivstellensätze; continuous version of Hilbert's 17th problem Scowcroft, P.: Some continuous positivstellensätze. J. algebra 124, 521-532 (1989) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) finite fields; number theory; algebraic number theory; computer science; coding theory; cryptography; algebraic geometry; discrete mathematics; polynomial factorization; counting points on curves; irreducible polynomials; primitive polynomials; bases; discrete logarithm; polynomial multiplication; algebraic curves; exponential sums; elliptic curves; recurrence sequences; cyclic codes; pseudo-random numbers; permutation polynomials; congruences; integer factorization; primality testing; computational algebraic number theory; algebraic complexity theory; polynomials with integer coefficients I. E. Shparlinski, \textit{Finite Fields: Theory and Computation}, Kluwer Academic Publ., Dordrecht, 1999 (to appear). | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) configuration of branches of an algebraic curve; Harnack theorem; number of limit cycles for a polynomial planar system; Hilbert's 16th problem | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) multilinear algebra; tensor products; algebraic varieties; secant varieties; representation theory; complexity theory; matrices; monograph; textbook; matrix multiplication; tensor decomposition; tensor network; border rank; tensor calculus; projective algebraic geometry; Terracini's Lemma; polynomial Waring problem; Segre varieties; signal processing; Littlewood-Richardson rule; Pieri's formula; Strassen's equation; Young flattening; Friedland's equation; Fano varieties of line; Chow varieties of zero cycle; Brill's equation; normal form; Konstant's theorem; Bott-Borel-Weil theorem; Koszul sequences; syzygies J. M. Landsberg, \textit{Tensors: Geometry and Applications}, American Mathematical Society, Providence, RI, 2012. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) étale cohomology; values of L-functions; Grothendieck's purity conjecture; Riemann-Roch problem; Atiyah-Bott fixed point formula; Tate conjecture; construction of a motivic cohomology theory; algebraic K- theory; topological K-theory; algebraic objects; stable homotopy objects Thomason, R. W.: Survey of algebraic versus étale topologicalK-theory,Algebraic K-Theory and Algebraic Number Theory, Contemporary Mathematics 83, Amer. Math. Soc., Providence (1989). | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) ordered fields; dense orbits property; automorphisms acting on spaces of orderings; behavior under field extensions; formally real field Gamboa J.\ M. and Recio T., Ordered fields with the dense orbits property, J. Pure Appl. Algebra 30 (1983), 237-246. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) zeta functions; distribution of zeros; \(L\)-functions; finite fields; automorphic \(L\)-functions; GUE measure; Montgomery-Odlyzko law; normalized spacings; Wigner measure; Kolmogoroff-Smirnov discrepancy function; generalized Sato-Tate conjecture; low-lying zeros; \(L\)-functions of elliptic curves; spacings of eigenvalues; Haar measure; Fredholm determinants; Deligne's equidistribution theorem; monodromy; Kloosterman sums N.M. Katz and P. Sarnak. \textit{Random matrices, Frobenius eigenvalues, and monodromy, vol. 45 of American Mathematical Society Colloquium Publications}. American Mathematical Society, Providence, RI (1999). | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real algebraic knots and links; encomplexed writhe; Hilbert's 16th problem Mikhalkin, G.; Orevkov, S., No article title, J. Knot Theory Ramifications, 25, 1642010, (2016) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) sum of squares; real closed field; real AP-curve Ruiz, J. M.: Pythagorean real curve germs. J. algebra 94, 126-144 (1985) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) fundamental domain; resolutions of cusp singularities; algorithms; totally real cubic fields; values of partial zeta-functions; Hilbert varieties Grundman, HG, Explicit resolutions of cubic cusp singularities, Math. Comp., 69, 815-825, (2000) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) hyperkähler variety; Calabi-Yau variety; arithmetic model; Brauer group; Artin's conjecture; \(K3\)-surface; abelian surface; Hilbert scheme of points; generalized Kummer variety; Hilbert modular surface | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's 16th problem; real algebraic hypersurfaces; Viro's patchworking; tropical hypersurfaces | 0 |
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