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Theorems · Theorem · number theory

HurwitzZeta.hasSum_int_cosZeta

∀ (a : ℝ) {s : ℂ},
  1 < s.re →
    HasSum (fun n => Complex.exp (2 * ↑Real.pi * Complex.I * ↑a * ↑n) / ↑|n| ^ s / 2) (HurwitzZeta.cosZeta (↑a) s)

Formula for cosZeta as a Dirichlet series in the convergence range, with sum over .

Defined in
Mathlib.NumberTheory.LSeries.HurwitzZetaEven
Cited by
1 results in Mathlib
Foundations
Depth 302 from the axioms · uses propext, Classical.choice, Quot.sound

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