Theorems · Theorem · number theory
HurwitzZeta.evenKernel_def
∀ (a x : ℝ),
↑(HurwitzZeta.evenKernel (↑a) x) =
Complex.exp (-↑Real.pi * ↑a ^ 2 * ↑x) * jacobiTheta₂ (↑a * Complex.I * ↑x) (Complex.I * ↑x)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- map_mulproof · cited by 1,137
- neg_negproof · cited by 960
- Complex.reproof · cited by 882
- Real.expproof · cited by 871
- Complex.Istatement and proof · cited by 866
- starRingEndproof · cited by 671
- neg_mulproof · cited by 654
- Complex.expstatement and proof · cited by 612
Cited by6
Results whose statement or proof uses this declaration.
- HurwitzZeta.hasSum_int_evenKernelproof · cited by 2
- HurwitzZeta.evenKernel_eq_cosKernel_of_zeroproof · cited by 1
- HurwitzZeta.evenKernel_negproof · cited by 1
- HurwitzZeta.evenKernel_undefproof · cited by 1
- HurwitzZeta.continuousOn_evenKernelproof · cited by 0
- HurwitzZeta.evenKernel_functional_equationproof · cited by 0