chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
2,280 | lean_file_chunk | a6eea4ea48ca68e781ceac4bd5ef0ebeb0601d6a9b3e3e7192ccde931e1ce173 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Koundinya Vajjha. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Koundinya Vajjha, Thomas Browning
-/
module
public import Mathlib.NumberTheory.Harmonic.Defs
public import Mathlib.NumberTheory.Padics.PadicNumbers
public import Mathlib.Tactic.Posi... |
11,186 | lean_file_chunk | 8512135ab34d8465405694c96b6206b4004eba687664311c83c7f33bc1d7f978 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.Convex.Deriv
public import Mathlib.Analysis.SpecialFunctions.Gamma.Deligne
public import Mathlib.Data.Nat.Factorial.Basic
publi... |
851 | lean_file_chunk | b259e7a03e5a258c188f1da3dc88aefc8871e8a6d08db60f621714a2f694732e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Koundinya Vajjha. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Koundinya Vajjha, Thomas Browning
-/
module
public import Mathlib.Data.Rat.Defs
public import Mathlib.Algebra.BigOperators.Group.Finset.Basic
/-!
This file defines the harmonic nu... |
19,687 | lean_file_chunk | 82949b54248521bdf683ec68a4ad2cc873ac459318cdac8be6bdd5231edba6ea | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.NumberTheory.LSeries.RiemannZeta
public import Mathlib.NumberTheory.Harmonic.GammaDeriv
/-!
# Asymptotics of `ζ s` as `s → 1`
The goal... |
7,370 | lean_file_chunk | b4e655eef3ff4bde8db037d8e3d7a63cb33618865c8882e622bda15e8d3cdaa9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.Complex.ExponentialBounds
public import Mathlib.Analysis.Normed.Order.Lattice
public import Mathlib.Analysis.SpecialFunctions.P... |
2,813 | lean_file_chunk | 800246be6d5ea3c6d7b3d98ea53b75e970afa720a7117aca8d2b1b0a079a2e29 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Arend Mellendijk. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Arend Mellendijk
-/
module
public import Mathlib.Analysis.SpecialFunctions.Integrals.Basic
public import Mathlib.Analysis.SumIntegralComparisons
public import Mathlib.NumberTheory.H... |
2,436 | lean_file_chunk | a01a8462930cca627c5686f584f20919d6f08caa7f8a511760b485e8bc646fdd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jou Glasheen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jou Glasheen, Kevin Buzzard
-/
module
public import Mathlib.Analysis.Normed.Field.ProperSpace
public import Mathlib.NumberTheory.Padics.RingHoms
/-!
# Properness of the p-adic numbers
... |
23,993 | lean_file_chunk | addaa90a2c3f2b5c467b99750348d41c483fcca16313957ffc0f1b23129534ff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
module
public import Mathlib.Algebra.Field.ZMod
public import Mathlib.NumberTheory.Padics.PadicIntegers
public import Mathlib.RingT... |
4,363 | lean_file_chunk | e1cd09ca70550797e97a3b2a3f36d93bab34bd7b8e43834dbb8272af5028bdb0 | lean_source_file | pkg_mathlib_source_file_chunks | (show (0 : ℝ) < (p : ℝ) ^ (-n : ℤ) from zpow_pos (mod_cast hp_prime.1.pos) _)
have := le_of_lt (hk (max n k) (le_max_right _ _))
rw [norm_le_pow_iff_mem_span_pow] at this
dsimp [lift]
rw [sub_eq_sub_add_sub (limNthHom f_compat r) _ ↑(nthHom f r (max n k))]
apply Ideal.add_mem _ _ this
rw [Ideal.mem_span_sin... |
20,241 | lean_file_chunk | 292710e4b37c82171e60c2acce432b12034eda95998db3dd93676d8cc5d7e323 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Mario Carneiro, Johan Commelin
-/
module
public import Mathlib.NumberTheory.Padics.PadicNumbers
public import Mathlib.RingTheory.DiscreteValuationRing.Basic
/-!
# p... |
12,318 | lean_file_chunk | 6c6ac4cdb0fc8c96b55a1f2c8025219b0e03fedb77f901931c684da85379bf06 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
module
public import Mathlib.Algebra.Order.AbsoluteValue.Basic
public import Mathlib.NumberTheory.Padics.PadicVal.Basic
/-!
# p-adic norm
This file defines the `... |
18,776 | lean_file_chunk | 2d08fe6fb8f50f5e3bee5b9c3d4816d96964e4dba3e53e3148f9a42e13348f6f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Giulio Caflisch, David Loeffler
-/
module
public import Mathlib.Algebra.Group.ForwardDiff
public import Mathlib.Analysis.Normed.Group.Ultra
public import Mathlib.NumberTheory.Padics.P... |
9,171 | lean_file_chunk | 5331e5a3a2a139eb344cf3edde7e0c131951af45b5d7dccaab94b79352a25a04 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Analysis.RCLike.Basic
public import Mathlib.NumberTheory.Padics.PadicIntegers
public import Mathlib.Topology.Algebra.Valued.ValuedFiel... |
23,971 | lean_file_chunk | 99ca4257bb6c35cf7af6f8144006389d0f3565c04e69e700aae5e84617fa00d0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
module
public import Mathlib.RingTheory.Valuation.Basic
public import Mathlib.NumberTheory.Padics.PadicNorm
public import Mathlib.Analysis.Normed.Field.Lemmas
publ... |
21,218 | lean_file_chunk | 1c9a93a7313647dcefa08556bd8b66632753ebe9a1db3e8b850ba62b8dc75707 | lean_source_file | pkg_mathlib_source_file_chunks | theorem add_eq_max_of_ne' {q r : ℚ_[p]} :
padicNormE q ≠ padicNormE r → padicNormE (q + r : ℚ_[p]) = max (padicNormE q) (padicNormE r) :=
Quotient.inductionOn₂ q r fun _ _ ↦ PadicSeq.add_eq_max_of_ne
@[simp]
theorem eq_padic_norm' (q : ℚ) : padicNormE (q : ℚ_[p]) = padicNorm p q :=
norm_const _
protected theo... |
10,278 | lean_file_chunk | 56aa804705d39434c8cad744ef0d7029c515f67f1c2710f054832e5869f18148 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández
-/
module
public import Mathlib.Analysis.Normed.Field.Dense
public import Mathlib.Analysis.Normed.Module.Completion
public import Mathli... |
1,344 | lean_file_chunk | 01de6bf46d199ad1ce938ba5a4ac1a63f1f3c3b664536c93a81e6715a4870f7b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.NumberTheory.Padics.PadicNumbers
public import Mathlib.RingTheory.Valuation.RankOne
/-!
# p-adic numbers with a valuative relation
#... |
12,088 | lean_file_chunk | 90dd14d54ba7c25bfa3235c0ad7c1372e31f64b57940fd2031dde23dac3c328c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Salvatore Mercuri. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salvatore Mercuri
-/
module
public import Mathlib.NumberTheory.Padics.WithVal
public import Mathlib.RingTheory.DedekindDomain.AdicValuation
public import Mathlib.RingTheory.Int.Bas... |
6,206 | lean_file_chunk | da65e5f04fd744b4d1f3d3ded3d94aad53d5ea51bc71ac0c665017130ddad6e8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.NumberTheory.Padics.MahlerBasis
public import Mathlib.Topology.Algebra.Monoid.AddChar
public import Mathlib.Analysis.SpecificLimits.Norm... |
21,254 | lean_file_chunk | aa4617329d4f0a429a06b2d74be425d6c0a5ec6fcb5cedcca4e0ce35b9ec4bd9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
module
public import Mathlib.Algebra.Polynomial.Identities
public import Mathlib.Analysis.SpecificLimits.Basic
public import Mathlib.NumberTheory.Padics.PadicInteg... |
14,215 | lean_file_chunk | 938354c13b5ba64ef94cb1c09a576d1359619875ffcdec04f72c8227e08250c6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.LinearAlgebra.Matrix.Integer
public import Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups
/-!
# Congruence subgroups
This defin... |
11,314 | lean_file_chunk | dbc1bf74c1332904ab72e2dc2c68283d576036347512ca3bbabaee36e5b71615 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups
public import Mathlib.NumberTheory.ModularForms.SlashActions
/-!
# Slash invariant forms
... |
9,476 | lean_file_chunk | 06a3ee41a59bad7fc8bdaaad581fc00fa96e287923e94c24f6b67c7f860c4b53 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Topology.Algebra.Group.Matrix
public import Mathlib.Topology.Algebra.IsUniformGroup.DiscreteSubgroup
public import Mathlib.Topology.Alge... |
8,764 | lean_file_chunk | 5591317392dcfa4bd23dc41b7d387e464f41fa6e89f5c71f0dc5762569c21584 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Analysis.Complex.SqrtDeriv
public import Mathlib.Analysis.Normed.Ring.InfiniteProd
public import Mathlib.NumberTheory.ModularForms.Dedek... |
23,995 | lean_file_chunk | 524d0a443886c98d6aa77d24e7552307dee99a438355cb9a9976d842d4357d90 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Algebra.DirectSum.Algebra
public import Mathlib.Analysis.Calculus.FDeriv.Star
public import Mathlib.Analysis.Complex.UpperHalfPlane.Mani... |
6,253 | lean_file_chunk | 79fe7c80f2ff60ad23661a13a18f12456775479607f2d34997373365ed471ed9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Seewoo Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Seewoo Lee
-/
module
public import Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.MDifferentiable
/-!
# Derivatives of modular forms
This file defines normalized derivative $D = ... |
6,294 | lean_file_chunk | 938816edc8ebc8f2a862f6c6aaedce8bfbb082c2116c9b4175e9f56b17b4b007 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.Complex.UpperHalfPlane.Topology
public import Mathlib.NumberTheory.ModularForms.QExpansion
/-!
# The Petersson scalar product
... |
7,529 | lean_file_chunk | 988a02b066d28da8e7a6d21ec7a5c93b02647fcf01887791e6e577aa239e721e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.NumberTheory.ModularForms.LevelOne
/-!
# Norm and trace maps
Given two subgroups `𝒢, ℋ` of `GL(2, ℝ)` with `𝒢.relindex ℋ ≠ 0` (i.e. ... |
7,197 | lean_file_chunk | 1b5f0f9879471503c498fe66a9dd1670a40c9e82e5fea3da381054d73ca8f633 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, David Loeffler
-/
module
public import Mathlib.Analysis.Calculus.LogDerivUniformlyOn
public import Mathlib.Analysis.Complex.LocallyUniformLimit
public import Mathlib.A... |
23,974 | lean_file_chunk | 04105f0187a653740b7a850761720025335bfbe864b78d6d1365ed8d5a8ada7a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.Complex.TaylorSeries
public import Mathlib.Analysis.Complex.UpperHalfPlane.Exp
public import Mathlib.NumberTheory.ModularForms.... |
2,331 | lean_file_chunk | b535a6d3ad606fb703fe9835a1406dbaeef8c55b25b7044211957440f4bd07e3 | lean_source_file | pkg_mathlib_source_file_chunks | apply FormalMultilinearSeries.le_radius_of_summable
simpa [norm_smul] using (hasSum_cuspFunction_of_hasSum_punctured hh hΓ hf (q := r)
(by simpa using hr) (mod_cast hr')).summable.norm
· simp
· intro y hy
rw [zero_add]
-- note the `simp`s below do not automatically apply this lemma to the argu... |
5,182 | lean_file_chunk | 94f064d2ccbdfffb81f6b4d2716cf74d408353dbc92f596590a64fc180b56ed4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty
public import Mathlib.NumberTheory.ModularForms.Cusps
public import Mathlib.Numb... |
4,802 | lean_file_chunk | 1de2a8c649934dd8c0cabfc5d7658b3935f9b0aa6d928fd3ed286c0bce8fbbdb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Analysis.Complex.AbsMax
public import Mathlib.LinearAlgebra.Matrix.FixedDetMatrices
public import Mathlib.NumberTheory.Modular
public im... |
2,446 | lean_file_chunk | 1d0c17d105ac898ea1f35d3858893d30ed5dd18168e2e70d7e00dc1f907b08f3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.NumberTheory.ModularForms.SlashInvariantForms
public import Mathlib.NumberTheory.ModularForms.CongruenceSubgroups
public import Mathlib.... |
20,652 | lean_file_chunk | 3202c7769dfb11736e2a938d0108019c9d2b934193e3ab7c36a2e0e2e7d08dec | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Algebra.EuclideanDomain.Int
public import Mathlib.Analysis.RCLike.Basic
public import Mathlib.NumberTheory.ModularForms.CongruenceSubgro... |
10,023 | lean_file_chunk | ac119d06c13a8511f2bfd3836de8f5de20ee4d91e0db950b33e547494182a64e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction
public import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Defs
public import Mathlib.L... |
310 | lean_file_chunk | 0e4d2eb2cacad9483454a7c2ac2a0f44aa608978a3a4ae4952041cdccab40bb3 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Analysis.Complex.SqrtDeriv
public import Mathlib.NumberTheory.ModularForms.DedekindEta
public import Mathlib.NumberTheory.ModularForms.Basic
public import Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform
deprecated_module (since := "2026-03-23") |
17,537 | lean_file_chunk | f7d3462e807a89285017e332bf5ed7baaf9c99f27ef715471ed1ad553ce77b58 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.NumberTheory.Modular
public import Mathlib.NumberTheory.ModularForms.Petersson
/-!
# Bounds for the norm of a modular form
We prove bo... |
11,725 | lean_file_chunk | 249cfd5084bb9cfbfe25f80c9eea3f6a99c354515ae60d0c7dd9a2a51dc3bbbe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.NumberTheory.ZetaValues
public import Mathlib.NumberTheory.LSeries.RiemannZeta
/-!
# Special values of Hurwitz and Riemann zeta functio... |
19,126 | lean_file_chunk | a981b02231807e648ff7f2970c3682de3cad3a78ee034d0508e50af06d6fefe6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.NumberTheory.DirichletCharacter.Bounds
public import Mathlib.NumberTheory.LSeries.Convolution
public import Mathlib.NumberTheory.LSeries.D... |
8,963 | lean_file_chunk | 678daeba50442f91736343a98bae381792c10fcfc6a06e6d159edb58aab23188 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Algebra.BigOperators.Field
public import Mathlib.Analysis.Normed.Ring.InfiniteSum
public import Mathlib.NumberTheory.ArithmeticFunction.De... |
11,101 | lean_file_chunk | ecac7969c11aa2f4b2c81c077e08b6bbbd990b36ae328873f874dfe9f2558be0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.NumberTheory.LSeries.HurwitzZeta
public import Mathlib.Analysis.PSeriesComplex
/-!
# Definition of the Riemann zeta function
## Main d... |
18,275 | lean_file_chunk | 7405555bf3d4394e38e930bfaadf8461af0fd996c73c185fb377ffc37e4ee5c0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler, Michael Stoll
-/
module
public import Mathlib.NumberTheory.LSeries.ZMod
public import Mathlib.NumberTheory.DirichletCharacter.Basic
public import Mathlib.NumberTheory.... |
20,852 | lean_file_chunk | 769d3f5a14a9e549bb87030f275c9f557d1c36de18585441e88f7c28e882ed4d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.MellinTransform
/-!
# Abstract functional equations for Mellin transforms
This file formalises a general version of an argume... |
2,939 | lean_file_chunk | fe81c4f42d47ed14ec3f4d5affacc9c8700b866f918a4d7843ef8cf2416f8216 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Huanyu Zheng. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Huanyu Zheng
-/
module
public import Mathlib.NumberTheory.LSeries.Nonvanishing
/-!
# Discreteness of the zeros of the Riemann zeta function
We show that the zeros of the Riemann zeta ... |
7,698 | lean_file_chunk | 9611c79f02d0d0f5e3b922bf5131f8368782a1a9f919d5c3cec6ff4b599b8325 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Analysis.Complex.LocallyUniformLimit
public import Mathlib.NumberTheory.LSeries.Convergence
public import Mathlib.Analysis.SpecialFunction... |
23,973 | lean_file_chunk | d722a375be35c43e0ec07ce61de4c2ec123879fc30ad1f156575f943c61f9389 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Data.ZMod.Coprime
public import Mathlib.NumberTheory.DirichletCharacter.Orthogonality
public import Mathlib.NumberTheory.LSeries.Linearity... |
2,643 | lean_file_chunk | 89525c2766ecf61dd0ca848455477b0390a4b1e5da47c97d355c3728ad4849af | lean_source_file | pkg_mathlib_source_file_chunks | variable {q : ℕ} [NeZero q] {a : ZMod q}
/-- **Dirichlet's Theorem** on primes in arithmetic progression: if `q` is a positive
integer and `a : ZMod q` is a unit, then there are infinitely many prime numbers `p`
such that `(p : ZMod q) = a`. -/
theorem infinite_setOf_prime_and_eq_mod (ha : IsUnit a) :
{p : ℕ | p.P... |
14,747 | lean_file_chunk | 4a75acaf9aa7c2e7ac368a7ddf2aeb5c1af402761002e2a39ffa3a14004edf63 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson, Michael Stoll
-/
module
public import Mathlib.Analysis.PSeries
public import Mathlib.Analysis.Normed.Module.FiniteDimension
public import Mathlib.LinearAlgebra.Complex... |
23,985 | lean_file_chunk | f63c06f28c03a386f9b34dd9635fcab7e18c143853e369ddae8f54d4b58baf73 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.NumberTheory.LSeries.AbstractFuncEq
public import Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds
public import Mathlib.Analysis.Sp... |
14,112 | lean_file_chunk | f1a110eb12fc1b5d2d7f47eda0a393190828cbbd93d4b26da01f3452cfe227ba | lean_source_file | pkg_mathlib_source_file_chunks | · simp only [h, Nat.cast_zero, aux, div_zero, zero_div, neg_zero, zero_add]
· simp only [ofReal_cos, ofReal_mul, ofReal_ofNat, ofReal_natCast, Complex.cos,
show 2 * π * a * n * I = 2 * π * I * a * n by ring, neg_mul, mul_div_assoc,
div_right_comm _ (2 : ℂ), Int.cast_natCast, Nat.abs_cast, Int.cast_neg, mu... |
7,767 | lean_file_chunk | 5668bb9051c0212c445c7c31545b027a34135793b8818acdc5830248bdd111d1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.Gamma.Deligne
/-!
# Dirichlet series as Mellin transforms
Here we prove general results of the form "the Mell... |
5,296 | lean_file_chunk | 833a18b99bd015196b97df13dd68fdc0786495e2e63371850225f95361f1c886 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Algebra.BigOperators.Field
public import Mathlib.NumberTheory.LSeries.Basic
/-!
# Linearity of the L-series of `f` as a function of `f`
... |
21,657 | lean_file_chunk | 9f5843bdbb2be693d383182339281ef14a48048a4072526640abfe276e71bdd4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.Analysis.Asymptotics.SpecificAsymptotics
public import Mathlib.Analysis.InnerProductSpace.Calculus
public import Mathlib.Analysis.SpecialF... |
5,274 | lean_file_chunk | 78e54a9353e456d96c7d17afb38ae23255b6f0b216769226615fd9e1de761385 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, David Loeffler, Michael Stoll
-/
module
public import Mathlib.Analysis.Complex.TaylorSeries
public import Mathlib.Analysis.Complex.Positivity
public import Mathlib.Numb... |
6,556 | lean_file_chunk | 58f19418f41e21d8f4ac64635f2cfb0101b6c52d3289492d8342bc64ae3c8d69 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.NumberTheory.LSeries.Basic
/-!
# Convergence of L-series
We define `LSeries.abscissaOfAbsConv f` ... |
12,082 | lean_file_chunk | 4dedcc0b67b217f407ba4c0de42bcdc974989a0d902c26281708f4bd53cfa489 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Analysis.Normed.Group.Tannery
public import Mathlib.NumberTheory.LSeries.Convergence
public import Mathlib.NumberTheory.LSeries.Linearity
... |
23,945 | lean_file_chunk | 0f34da8cf7ecbf0623890231e75f28b7b74d1ff596f25926aafdb12540c5324e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.NumberTheory.LSeries.AbstractFuncEq
public import Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds
public import Mathlib.NumberTheor... |
3,601 | lean_file_chunk | a2845067200d2791c6a2e75bac33a2dcfe69f6d9816f6835ab4644be020d508d | lean_source_file | pkg_mathlib_source_file_chunks | suffices ∀ b : ℝ, 0 ≤ b → SignType.sign (n + b) / (↑|n + b| : ℂ) ^ s = 1 / (n + b) ^ s by
simp only [add_sub_assoc, this a ha.1, this (1 - a) (sub_nonneg.mpr ha.2), push_cast]
intro b hb
rw [abs_of_nonneg (by positivity), (by simp : (n : ℂ) + b = ↑(n + b))]
rcases lt_or_eq_of_le (by positivity : 0 ≤ n + b) wi... |
23,938 | lean_file_chunk | 430fb034b10c46dc650c7897287ea1f64ac0f7ff72fc6a45954eaaa0bf4721e0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.Fourier.ZMod
public import Mathlib.Analysis.Normed.Module.Connected
public import Mathlib.NumberTheory.LSeries.RiemannZeta
/-!... |
3,230 | lean_file_chunk | 9b9fc52d337adfcfa1653342b646bbdb7ce31c29bdd5c60aebd3ca197cbdd1a3 | lean_source_file | pkg_mathlib_source_file_chunks | have h2U : 2 ∈ U := ⟨.inl two_ne_zero, .inl (OfNat.ofNat_ne_one _)⟩
have hUo : IsOpen U := (isOpen_compl_singleton.union isOpen_const).inter
(isOpen_compl_singleton.union isOpen_const)
have hUp : IsPreconnected U := by
-- need to write `U` as the complement of an obviously countable set
let Uc : Set ℂ :... |
20,877 | lean_file_chunk | 3f75591bb1091f89f4e5e39856f58b0d8686648062d341ad32edb35cee81864f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll, David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.Complex.LogBounds
public import Mathlib.NumberTheory.Harmonic.ZetaAsymp
public import Mathlib.Nu... |
8,321 | lean_file_chunk | 8f0495e16c16ddf4766b1014c1d217c23debf4a86b8d4b8d1ab0450e36edd417 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.NumberTheory.LSeries.HurwitzZetaEven
public import Mathlib.NumberTheory.LSeries.HurwitzZetaOdd
public import Mathlib.Analysis.SpecialFun... |
10,718 | lean_file_chunk | 89e137a2a91752cce6e85aea56caa7bec8de53cd928991a2c9be4ca08bf14d8a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Michael Stoll
-/
module
public import Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic
/-!
# Legendre symbol
This file contains results about Legendre symbols.
W... |
13,137 | lean_file_chunk | b2ebbab2852f4c044c22df78d143640f889728ddbf3c0977101615baf8aeca25 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots
public import Mathlib.FieldTheory.Finite.Trace
public import Mathlib.Algebra.Group.AddChar
public i... |
6,445 | lean_file_chunk | 23ce05eeea7d75b7bfb62de8f0c197d156594d5b241e18c030aea4731db339a3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Michael Stoll
-/
module
public import Mathlib.NumberTheory.LegendreSymbol.Basic
public import Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum
/-!
# Quadratic r... |
11,479 | lean_file_chunk | 407bf025db9fdb426ed9eb6af09ebc493897ec3d7aea04a35a0721c454e5dc06 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
module
public import Mathlib.Data.Nat.Prime.Factorial
public import Mathlib.NumberTheory.LegendreSymbol.Basic
/-!
# Lemmas of Gauss and Eisenstein
This file contains t... |
6,489 | lean_file_chunk | d8e8c000dfa75636a0a3eedb6dae673f504a970d4005f787851b390701d9aead | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Data.Int.Range
public import Mathlib.Data.ZMod.Basic
public import Mathlib.NumberTheory.MulChar.Basic
/-!
# Quadratic characters on ℤ/nℤ
... |
23,988 | lean_file_chunk | 7e02572af611891d1f7f3326e8611019faf45ff36ab0ad5aaa364149263f6eb0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll, Thomas Zhu, Mario Carneiro
-/
module
public import Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity
/-!
# The Jacobi Symbol
We define the Jacobi symbol and pro... |
2,279 | lean_file_chunk | 11bb5b026d421d9a335d189df3aa679e600003ac1685e7aee36cff273a347595 | lean_source_file | pkg_mathlib_source_file_chunks | by_cases h : a % 4 = 3 ∧ b % 4 = 3 <;> simp [h]; cases flip <;> simp
/-- Computes `J(a | b)` by reducing `b` to odd by repeated division and then using
`fastJacobiSymAux`. -/
private def fastJacobiSym (a : ℤ) (b : ℕ) : ℤ :=
if hb0 : b = 0 then
1
else if _ : b % 2 = 0 then
if a % 2 = 0 then
0
else... |
7,781 | lean_file_chunk | 5e9c3ceab746ed325bfee78118670dd2646b4cf55329b6827ca7bc7d5b3ba7a1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
module
public import Mathlib.NumberTheory.ArithmeticFunction.Defs
/-!
# The arithmetic function `ζ`
We define `ζ` to be the arithmetic function with `ζ n = 1` for ... |
15,072 | lean_file_chunk | 018cb0a33cba86f998867141191e5021be60991c4c5163f2bbd739a49f56f9d0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.NumberTheory.ArithmeticFunction.Defs
public import Mathlib.NumberTheory.Height.Northcott
public import Mathlib.RingTheory.PowerSeries.... |
5,921 | lean_file_chunk | 773acc5612c97f7ae2c94f5c4b70803889a47bde7b10f64ef719397e18802777 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.Analysis.SpecialFunctions.Log.Basic
public import Mathlib.Data.Nat.Cast.Field
public import Mathlib.NumberTheory.ArithmeticFunction.Moebius
... |
14,649 | lean_file_chunk | cd39a8db211e7822a26ac1e323e15950269881b4668e297776894522b21cf9d4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
module
public import Mathlib.Algebra.Order.Ring.Abs
public import Mathlib.NumberTheory.ArithmeticFunction.Misc
/-!
# The Möbius function and Möbius inversion
## Mai... |
23,597 | lean_file_chunk | 5f2e3c0ee53354cbd40ad76c1728c0bd334f892dbb9dd12980d4d99c9e4eb98b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
module
public import Mathlib.Algebra.Algebra.Defs
public import Mathlib.Algebra.Module.BigOperators
public import Mathlib.Data.Nat.Factorization.Induction
public imp... |
16,228 | lean_file_chunk | 1f643204719664c35e2fbced92312892813d618d6946f15b995f57748f01adbb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
module
public import Mathlib.NumberTheory.ArithmeticFunction.Zeta
public import Mathlib.Data.Nat.Factorization.PrimePow
/-!
# Miscellaneous arithmetic Functions
Thi... |
6,440 | lean_file_chunk | 95ce1357ad3837cba8ba8e361c7bf866ba710da5937a3219eac8895b6269c32e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Snir Broshi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Snir Broshi
-/
module
public import Mathlib.Algebra.GCDMonoid.FinsetLemmas
public import Mathlib.NumberTheory.ArithmeticFunction.Defs
public import Mathlib.RingTheory.ZMod.UnitsCyclic
/... |
3,902 | lean_file_chunk | c15d0af0f016ebf426334339de442ca0de1c244861a4946faf66da78a841a9b7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.FieldTheory.Finite.Basic
public import Mathlib.NumberTheory.DirichletCharacter.Basic
public import Mathlib.NumberTheory.MulChar.Duality
/... |
3,186 | lean_file_chunk | 5b1cf78dbad6906de4e669517dbee546e3f36be6857fe44d4ae6bf133d961ea3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.NumberTheory.DirichletCharacter.Basic
public import Mathlib.NumberTheory.GaussSum
/-!
# Gauss sums for Dirichlet characters
-/
public ... |
19,151 | lean_file_chunk | f5a0b7ea47cb2eb018c11a6772282f8f4a211e253e7c952d58084944d790dbf9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Ashvni Narayanan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ashvni Narayanan, Moritz Firsching, Michael Stoll
-/
module
public import Mathlib.Algebra.Group.EvenFunction
public import Mathlib.Data.ZMod.Units
public import Mathlib.NumberTheory... |
1,293 | lean_file_chunk | 7363a25e91df25cb1c5139a35181205e71870250a0663b9df87bada2beb8619e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Analysis.Normed.Field.Basic
public import Mathlib.FieldTheory.Finite.Basic
public import Mathlib.NumberTheory.DirichletCharacter.Basic
/-... |
7,659 | lean_file_chunk | 75d920b0d5ccee74f08ed369842c4b657c5b58eb8acb7d98eb1893d48738bb65 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Alexey Soloyev, Junyan Xu, Kamila Szewczyk
-/
module
public import Mathlib.Algebra.EuclideanDomain.Basic
public import Mathlib.Algebra.LinearRecurrence
public impo... |
19,717 | lean_file_chunk | 64c5acbfc7e63a330b00c8f5eef34c4945eabd5e687128e242e5405ee8714381 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Abhimanyu Pallavi Sudhir, Jean Lo, Calle Sönne, Yury Kudryashov
-/
module
public import Mathlib.Algebra.Algebra.Rat
public import Mathlib.Data.Nat.Prime.Int
public imp... |
11,001 | lean_file_chunk | 477213e4aeeef36c61ec46ba7ca96457d9e4157ef66c4c2bcdfc393cc569c5bf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
module
public import Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots
public import Mathlib.RingTheory.DedekindDomain.Dvr
public import Mathlib.NumberTheory.NumberFi... |
23,979 | lean_file_chunk | 0ee2908731f3393eb7f4fb68574418f62e432110dc525af5c1d5abe38ba82714 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
module
public import Mathlib.RingTheory.Polynomial.Cyclotomic.Roots
public import Mathlib.NumberTheory.NumberField.Basic
public import Mathlib.FieldTheory.Separabl... |
22,334 | lean_file_chunk | a0cfb6f300f978de14efdbee935d94fe64205f4af3cf2bf7326fbf08fa1ea3ba | lean_source_file | pkg_mathlib_source_file_chunks | Polynomial.map_X]
obtain ⟨z, hz⟩ := ((isCyclotomicExtension_iff _ _ _).1 H).1 hS (NeZero.ne _)
exact X_pow_sub_one_splits hz
/-- A cyclotomic extension splits `cyclotomic n K` if `n ∈ S`. -/
theorem splits_cyclotomic [IsCyclotomicExtension S K L] (hS : n ∈ S) :
Splits ((cyclotomic n K).map (algebraMap K L)) :=... |
6,783 | lean_file_chunk | 8a6bf599271d059cbe4a61aa4c5d6e19d8c41608748800bcc48121fff4522e6a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
module
public import Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots
public import Mathlib.FieldTheory.PolynomialGaloisGroup
/-!
# Galois group of cyclotomic extensi... |
16,613 | lean_file_chunk | c96941061836ae88248a904a07eae3291b2dc6abef0a1536e16a80177c8d5a9a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Hanneke Wiersema. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Buzzard, Hanneke Wiersema, Andrew Yang
-/
module
public import Mathlib.Algebra.Ring.Aut
public import Mathlib.NumberTheory.Padics.RingHoms
public import Mathlib.RingTheory.Roo... |
23,938 | lean_file_chunk | c1df4615159dbebd4d99829438305dd560ad2d5902178c204ad86a2307c33c3b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best, Riccardo Brasca, Eric Rodriguez
-/
module
public import Mathlib.Data.Nat.Factorization.LCM
public import Mathlib.Data.Nat.Factorization.PrimePow
public import Mathlib.D... |
3,880 | lean_file_chunk | 097632cbe2e4172376a4853a3022f50c9905007ef296d6bdaf27ff27f917ebff | lean_source_file | pkg_mathlib_source_file_chunks | /-- If `Irreducible (cyclotomic (p ^ (k + 1)) K)` (in particular for `K = ℚ`) and `p` is a prime,
then the norm of `ζ ^ (p ^ s) - 1` is `p ^ (p ^ s)` if `k ≠ 0` and `s ≤ k`. -/
theorem norm_pow_sub_one_eq_prime_pow_of_ne_zero {k s : ℕ} (hζ : IsPrimitiveRoot ζ (p ^ (k + 1)))
[hpri : Fact p.Prime] [hcycl : IsCyclotom... |
3,705 | lean_file_chunk | 5b281f09185251374f876dcacad55348225305d5d753fae277c0bec51ee3f6d3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.LinearAlgebra.Projectivization.Basic
public import Mathlib.NumberTheory.Height.Basic
/-!
# Heights of points in projective space
We defi... |
23,984 | lean_file_chunk | 5cbe97549f168d0238a5afdfea6939e900e6fa21a5c77a479c4199cdfca0461c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Analysis.SpecialFunctions.Log.PosLog
public import Mathlib.Tactic.Positivity.Core
import Mathlib.Algebra.FiniteSupport.Basic
import Mathl... |
12,605 | lean_file_chunk | b0c3e9425a04aa4a13762385f98475ce9c303d007e89503bf7fe89d6b9f20c3c | lean_source_file | pkg_mathlib_source_file_chunks | lemma logHeight₁_pow (x : K) (n : ℕ) : logHeight₁ (x ^ n) = n * logHeight₁ x := by
simp only [logHeight₁_eq_log_mulHeight₁, mulHeight₁_pow, log_pow]
/-- The multiplicative height of the `n`th power of a field element `x` (with `n : ℤ`)
is the `|n|`th power of the multiplicative height of `x`. -/
lemma mulHeight₁_zpo... |
23,991 | lean_file_chunk | 0714e1c60378230f298120abd50c601686a4ed322bcfa165287ef165cf1f9da0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Algebra.Polynomial.Homogenize
public import Mathlib.NumberTheory.Height.Basic
import Mathlib.Algebra.Order.Ring.IsNonarchimedean
import M... |
4,030 | lean_file_chunk | e662faea7fffc508a51a5cf3d9984656884772fb83f351d9805032b2e3bc8af2 | lean_source_file | pkg_mathlib_source_file_chunks | We show that the multiplicative height of `![a*c, a*d + b*c, b*d]` is bounded from above and from
below by a positive constant times the product of the multiplicative heights of `![a, b]` and
`![c, d]` (and the analogous statements for the logarithmic heights).
The constants are unspecified here; with (likely consider... |
1,731 | lean_file_chunk | 4863f131feeaca0e99cc29cd5590d5d0d3a1b652358b133107a65b2d6096596c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.Order.Filter.Cofinite
/-!
# Northcott Functions
In number theory, the height function `h` satisfies the *Northcott property* that th... |
7,880 | lean_file_chunk | b51d15bf47a510027113b5081eabc5ae605cd928c754a743be97fad47eb4415b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll, Ralf Stephan
-/
module
public import Mathlib.NumberTheory.NumberField.ProductFormula
public import Mathlib.NumberTheory.Height.Basic
/-!
# Heights over number fields
W... |
16,466 | lean_file_chunk | 4cd46eb659a4a53b3fd29781bf67329d87a4bb5859712ca312caf24d850ba668 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
public import Mathlib.LinearAlgebra.FreeModule.PID
public import Mathlib.LinearAlgebra.Matrix.AbsoluteValue... |
5,632 | lean_file_chunk | e6553748f363cc7c6b8acef5d00892ff6e36777f6a87a56ffa75b5e985412d88 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Combinatorics.Pigeonhole
public import Mathlib.Algebra.Order.AbsoluteValue.Euclidean
/-!
# Admissible a... |
2,450 | lean_file_chunk | 1cfa68598d1ff6c6fca752668cd0f1b5dd27a3da0d780cb6bbae2a25858ba4c7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.Algebra.Algebra.Basic
public import Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue
public import Mathlib.Data.Real.Archimedean
/-!
... |
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