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Theorems · Theorem · number theory

DirichletCharacter.LSeries_eulerProduct_hasProd

∀ {s : ℂ} {N : ℕ} (χ : DirichletCharacter ℂ N),
  1 < s.re → HasProd (fun p => (1 - χ ↑↑p * ↑↑p ^ (-s))⁻¹) (LSeries (fun n => χ ↑n) s)

The Euler product for Dirichlet L-series, valid for s.re > 1. This version is stated in terms of HasProd.

Defined in
Mathlib.NumberTheory.EulerProduct.DirichletLSeries
Cited by
2 results in Mathlib
Foundations
Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

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