Theorems · Theorem · number theory
DirichletCharacter.differentiableAt_LFunction
∀ {N : ℕ} [inst : NeZero N] (χ : DirichletCharacter ℂ N) (s : ℂ),
s ≠ 1 ∨ χ ≠ 1 → DifferentiableAt ℂ (DirichletCharacter.LFunction χ) sThe L-function of a Dirichlet character is differentiable, except at s = 1 if the character is
trivial.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 306 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Complexstatement and proof · cited by 5,565
- ZModstatement · cited by 1,024
- DifferentiableAtstatement · cited by 617
- DirichletCharacterstatement and proof · cited by 161
- DirichletCharacter.LFunctionstatement · cited by 23
- MulChar.sum_eq_zero_of_ne_oneproof · cited by 9
- ZMod.differentiableAt_LFunctionproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- DirichletCharacter.differentiable_LFunctionproof · cited by 2
- DirichletCharacter.differentiable_LFunctionTrivChar₁proof · cited by 1
- DirichletCharacter.deriv_LFunctionTrivChar₁_apply_of_ne_oneproof · cited by 1
- DirichletCharacter.LFunction_isBigO_horizontalproof · cited by 0