Theorems · Definition · number theory
HurwitzZeta.completedSinZeta
UnitAddCircle → ℂ → ℂ
The entire function of s which agrees with
Gamma ((s + 1) / 2) * π ^ (-(s + 1) / 2) * ∑' (n : ℕ), sin (2 * π * a * n) / n ^ s
for 1 < re s.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 301 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- UnitAddCirclestatement and proof · cited by 157
- WeakFEPair.symmproof · cited by 24
- WeakFEPair.Λproof · cited by 20
- HurwitzZeta.hurwitzOddFEPairproof · cited by 8
Cited by11
Results whose statement or proof uses this declaration.
- HurwitzZeta.sinZetaproof · cited by 17
- HurwitzZeta.sinZeta_negproof · cited by 4
- HurwitzZeta.hurwitzZetaOdd_one_subproof · cited by 2
- HurwitzZeta.hasSum_int_completedSinZetastatement · cited by 2
- HurwitzZeta.completedSinZeta_one_substatement · cited by 1
- HurwitzZeta.sinZeta_one_subproof · cited by 1
- HurwitzZeta.completedHurwitzZetaOdd_one_substatement and proof · cited by 1
- HurwitzZeta.completedSinZeta_negstatement · cited by 1
- HurwitzZeta.differentiable_completedSinZetastatement · cited by 1
- HurwitzZeta.sinZeta_neg_two_mul_nat_sub_oneproof · cited by 0
- HurwitzZeta.hasSum_nat_completedSinZetastatement and proof · cited by 0