Theorems · Theorem · number theory
HurwitzZeta.hasSum_nat_sinKernel
∀ (a : ℝ) {t : ℝ},
0 < t →
HasSum (fun n => 2 * ↑n * Real.sin (2 * Real.pi * a * ↑n) * Real.exp (-Real.pi * ↑n ^ 2 * t))
(HurwitzZeta.sinKernel (↑a) t)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
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
- Complexproof · cited by 5,565
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Real.pistatement and proof · cited by 1,774
- mul_assocproof · cited by 1,667
- Complex.ofRealproof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- neg_negproof · cited by 960
Cited by1
Results whose statement or proof uses this declaration.
- HurwitzZeta.isBigO_atTop_sinKernelproof · cited by 0