Real ultraflat Littlewood polynomials and unbounded binary merit factors
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
Scope
The formalization gives real Littlewood polynomials of every sufficiently large length whose maximum modulus on the unit circle is at most $(1+\eta)\sqrt N$ for any fixed $\eta>0$. Thus the smallest possible maximum is asymptotically minimal through all integer lengths.
A further statement chooses one family of real sign polynomials for all lengths such that, for every fixed finite $p>0$, the $L^p$ mean of $\bigl||P_N(z)|/\sqrt N-1\bigr|$ on the unit circle tends to zero. The results are existential and do not give an effective convergence rate or a signing algorithm.
Comparator links
| Result | Comparator statement |
|---|---|
| Asymptotically minimal Littlewood maximum | AsymptoticallyMinimalLittlewood.lean |
| Finite-exponent flatness of one all-length Littlewood family | LittlewoodFiniteFlatness.lean |