Theorems · Theorem · number theory
HurwitzZeta.differentiableAt_cosZeta
∀ (a : UnitAddCircle) {s : ℂ}, s ≠ 1 ∨ a ≠ 0 → DifferentiableAt ℂ (HurwitzZeta.cosZeta a) sThe cosine zeta function is differentiable everywhere, except at s = 1 if a = 0.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 302 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Compl.complproof · cited by 2,925
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- one_ne_zeroproof · cited by 885
- div_eq_mul_invproof · cited by 715
- DifferentiableAtstatement · cited by 617
- AddSubgroup.zmultiplesstatement · cited by 493
- IsOpen.mem_nhdsproof · cited by 470
- Function.update_of_neproof · cited by 198
- UnitAddCirclestatement and proof · cited by 157
Cited by2
Results whose statement or proof uses this declaration.
- HurwitzZeta.differentiableAt_expZetaproof · cited by 2
- HurwitzZeta.differentiable_cosZeta_of_ne_zeroproof · cited by 0