differentiable_LFunction — Mathlib

English

The L-function of a nontrivial Dirichlet character is differentiable everywhere.

Русский

L-функция ненулевого персонажа Диерихле дифференцируема везде.

LaTeX

$$differentiable_LFunction (χ) (∀ χ ≠ 1) → Differentiable ℂ (LFunction χ)$$

Lean4

/-- The L-function of a non-trivial Dirichlet character is differentiable everywhere. -/
@[fun_prop]
theorem differentiable_LFunction {χ : DirichletCharacter ℂ N} (hχ : χ ≠ 1) : Differentiable ℂ (LFunction χ) :=
  (differentiableAt_LFunction _ · <| Or.inr hχ)

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