Theorems · Theorem · number theory
DirichletCharacter.differentiable_LFunction
∀ {N : ℕ} [inst : NeZero N] {χ : DirichletCharacter ℂ N}, χ ≠ 1 → Differentiable ℂ (DirichletCharacter.LFunction χ)The L-function of a non-trivial Dirichlet character is differentiable everywhere.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 307 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- ZModstatement · cited by 1,024
- Differentiablestatement · cited by 298
- DirichletCharacterstatement and proof · cited by 161
- DirichletCharacter.LFunctionstatement · cited by 23
- DirichletCharacter.differentiableAt_LFunctionproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- DirichletCharacter.LFunction_changeLevelproof · cited by 1
- DirichletCharacter.continuousOn_neg_logDeriv_LFunction_of_nontrivproof · cited by 1