Theorems · Theorem · number theory
HurwitzZeta.cosKernel_def
∀ (a x : ℝ), ↑(HurwitzZeta.cosKernel (↑a) x) = jacobiTheta₂ (↑a) (Complex.I * ↑x)
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Complex.ofRealstatement and proof · cited by 1,654
- map_mulproof · cited by 1,137
- neg_negproof · cited by 960
- Complex.Istatement and proof · cited by 866
- starRingEndproof · cited by 671
- neg_mulproof · cited by 654
- AddSubgroup.zmultiplesstatement · cited by 493
- QuotientAddGroup.mkstatement and proof · cited by 348
- mul_div_cancel_right₀proof · cited by 70
- Complex.conj_ofRealproof · cited by 41
Cited by6
Results whose statement or proof uses this declaration.
- HurwitzZeta.hasSum_int_cosKernelproof · cited by 2
- HurwitzZeta.cosKernel_negproof · cited by 1
- HurwitzZeta.evenKernel_eq_cosKernel_of_zeroproof · cited by 1
- HurwitzZeta.cosKernel_undefproof · cited by 1
- HurwitzZeta.continuousOn_cosKernelproof · cited by 0
- HurwitzZeta.evenKernel_functional_equationproof · cited by 0