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 ℤ.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 302 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- absstatement and proof · cited by 1,814
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- Complex.restatement and proof · cited by 882
- Complex.Istatement and proof · cited by 866
- Complex.expstatement and proof · cited by 612
- zero_lt_oneproof · cited by 598
- HasSumstatement and proof · cited by 518
- AddSubgroup.zmultiplesstatement · cited by 493
Cited by1
Results whose statement or proof uses this declaration.
- HurwitzZeta.hasSum_nat_cosZetaproof · cited by 4