Theorems · Theorem · number theory
HurwitzZeta.hasSum_int_sinKernel
∀ (a : ℝ) {t : ℝ},
0 < t →
HasSum
(fun n =>
-Complex.I * ↑n * Complex.exp (2 * ↑Real.pi * Complex.I * ↑a * ↑n) * ↑(Real.exp (-Real.pi * ↑n ^ 2 * t)))
↑(HurwitzZeta.sinKernel (↑a) t)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
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
- one_mulproof · cited by 2,841
- mul_commproof · cited by 2,262
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Real.pistatement and proof · cited by 1,774
- mul_assocproof · cited by 1,667
- Complex.ofRealstatement and proof · cited by 1,654
- neg_negproof · cited by 960
- Real.expstatement and proof · cited by 871
- Complex.Istatement and proof · cited by 866
- neg_mulproof · cited by 654
Cited by2
Results whose statement or proof uses this declaration.
- HurwitzZeta.hasSum_int_completedSinZetaproof · cited by 2
- HurwitzZeta.hasSum_nat_sinKernelproof · cited by 1