Theorems · Theorem · number theory
tendsto_riemannZeta_sub_one_div
Filter.Tendsto (fun s => riemannZeta s - 1 / (s - 1)) (nhdsWithin 1 {1}ᶜ) (nhds ↑Real.eulerMascheroniConstant)The function ζ s - 1 / (s - 1) tends to γ as s → 1.
- Defined in
- Mathlib.NumberTheory.Harmonic.ZetaAsymp
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 307 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites53
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realproof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Compl.complstatement and proof · cited by 2,925
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- mul_commproof · cited by 2,262
- nhdsWithinstatement and proof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Complex.ofRealstatement and proof · cited by 1,654
Cited by3
Results whose statement or proof uses this declaration.
- differentiable_riemannZeta₀proof · cited by 5
- ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_Gammaℝproof · cited by 1
- isBigO_riemannZeta_sub_one_divproof · cited by 0