Theorems · Theorem · number theory
HurwitzZeta.sinKernel_def
∀ (a x : ℝ), ↑(HurwitzZeta.sinKernel (↑a) x) = jacobiTheta₂' (↑a) (Complex.I * ↑x) / (-2 * ↑Real.pi)
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- Complex.Istatement and proof · cited by 866
- starRingEndproof · cited by 671
- neg_mulproof · cited by 654
- AddSubgroup.zmultiplesstatement · cited by 493
- map_negproof · cited by 378
Cited by5
Results whose statement or proof uses this declaration.
- HurwitzZeta.sinKernel_negproof · cited by 2
- HurwitzZeta.hasSum_int_sinKernelproof · cited by 2
- HurwitzZeta.sinKernel_undefproof · cited by 1
- HurwitzZeta.continuousOn_sinKernelproof · cited by 0
- HurwitzZeta.oddKernel_functional_equationproof · cited by 0