Theorems · Theorem · number theory
DirichletCharacter.norm_le_one
∀ {F : Type u_1} [inst : NormedField F] {n : ℕ} (χ : DirichletCharacter F n) (a : ZMod n), ‖χ a‖ ≤ 1The values of a Dirichlet character with target a normed field have norm bounded by 1.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- IsUnitproof · cited by 1,602
- NormedFieldstatement and proof · cited by 1,084
- ZModstatement and proof · cited by 1,024
- Eq.leproof · cited by 605
- norm_zeroproof · cited by 366
- zero_le_oneproof · cited by 316
- IsUnit.unitproof · cited by 252
- DirichletCharacterstatement and proof · cited by 161
- MulChar.map_nonunitproof · cited by 13
Cited by7
Results whose statement or proof uses this declaration.
- summable_dirichletSummandproof · cited by 3
- DirichletCharacter.LSeriesSummable_mulproof · cited by 2
- DirichletCharacter.LSeriesSummable_of_one_lt_reproof · cited by 2
- DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpowproof · cited by 1
- DirichletCharacter.eulerProduct_log_eq_LSeriesproof · cited by 1
- DirichletCharacter.LSeries_changeLevelproof · cited by 0
- DirichletCharacter.LSeriesSummable_zetaMulproof · cited by 0