Theorems · Theorem · number theory
riemannZeta_residue_one
Filter.Tendsto (fun s => (s - 1) * riemannZeta s) (nhdsWithin 1 {1}ᶜ) (nhds 1)The residue of ζ(s) at s = 1 is equal to 1.
- Defined in
- Mathlib.NumberTheory.LSeries.RiemannZeta
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 304 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Complexstatement · cited by 5,565
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- Compl.complstatement · cited by 2,925
- nhdsWithinstatement · cited by 1,912
- riemannZetastatement · cited by 85
- HurwitzZeta.hurwitzZetaEven_residue_oneproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- tendsto_riemannZeta_sub_one_divproof · cited by 3
- DirichletCharacter.LFunctionTrivChar_residue_oneproof · cited by 2
- tendsto_sub_mul_tsum_nat_cpowproof · cited by 1
- riemannZeta_eventually_ne_zero_nhds_oneproof · cited by 0