LFunction_neg_two_mul_nat — Mathlib

English

The L-function of an even Dirichlet character vanishes at negative even integers: LFunction χ (−2n) = 0.

Русский

L-функция чётного Dirichlet-персонажа обнуляется на отрицательных чётных целых: LFunction χ (−2n) = 0.

LaTeX

$$LFunction χ (−2n) = 0$$

Lean4

/-- The L-function of an even Dirichlet character vanishes at strictly negative even integers. -/
@[simp]
theorem LFunction_neg_two_mul_nat {χ : DirichletCharacter ℂ N} (hχ : Even χ) (n : ℕ) [NeZero n] :
    LFunction χ (-(2 * n)) = 0 :=
  by
  obtain ⟨m, rfl⟩ := Nat.exists_eq_succ_of_ne_zero (NeZero.ne n)
  exact_mod_cast hχ.LFunction_neg_two_mul_nat_add_one m

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