Theorems · Definition · number theory
HurwitzZeta.completedHurwitzZetaOdd
UnitAddCircle → ℂ → ℂ
The entire function of s which agrees with
1 / 2 * Gamma ((s + 1) / 2) * π ^ (-(s + 1) / 2) * ∑' (n : ℤ), sgn (n + a) / |n + a| ^ s
for 1 < re s.
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 301 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- UnitAddCirclestatement and proof · cited by 157
- WeakFEPair.Λproof · cited by 20
- HurwitzZeta.hurwitzOddFEPairproof · cited by 8
Cited by18
Results whose statement or proof uses this declaration.
- HurwitzZeta.hurwitzZetaOddproof · cited by 21
- ZMod.completedLFunctionproof · cited by 14
- HurwitzZeta.hurwitzZetaOdd_negproof · cited by 5
- ZMod.completedLFunction₀proof · cited by 4
- HurwitzZeta.hurwitzZetaOdd_one_subproof · cited by 2
- HurwitzZeta.completedHurwitzZetaOdd_negstatement · cited by 2
- ZMod.completedLFunction_def_evenproof · cited by 2
- HurwitzZeta.differentiable_completedHurwitzZetaOddstatement · cited by 2
- HurwitzZeta.hurwitzZetaOdd_neg_two_mul_nat_sub_oneproof · cited by 1
- HurwitzZeta.hasSum_int_completedHurwitzZetaOddstatement · cited by 1
- HurwitzZeta.completedHurwitzZetaOdd_one_substatement · cited by 1
- HurwitzZeta.completedSinZeta_one_substatement and proof · cited by 1