LSeriesSummable_twist_vonMangoldt

English

The L-series of the twist of the von Mangoldt function Λ by a Dirichlet character χ converges at s when Re(s) > 1: LSeriesSummable (χ * Λ) s.

Русский

L-серия twist Λ по χ сходится при Re(s) > 1: LSeriesSummable (χ * Λ) s.

LaTeX

$$$1 < \\operatorname{Re}(s) \\Rightarrow LSeriesSummable(\\uparrow χ * \\uparrow Λ)\\;s$$$

Lean4

/-- The L-series of the twist of the von Mangoldt function `Λ` by a Dirichlet character `χ`
converges at `s` when `re s > 1`. -/
theorem LSeriesSummable_twist_vonMangoldt {N : ℕ} (χ : DirichletCharacter ℂ N) {s : ℂ} (hs : 1 < s.re) :
    LSeriesSummable (↗χ * ↗Λ) s :=
  LSeriesSummable_mul χ <| LSeriesSummable_vonMangoldt hs

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