Theorems · Theorem · number theory
tendsto_sub_mul_tsum_nat_cpow
Filter.Tendsto (fun s => (s - 1) * ∑' (n : ℕ), 1 / ↑n ^ s) (nhdsWithin 1 {s | 1 < s.re}) (nhds 1)The residue of ζ(s) at s = 1 is equal to 1, expressed using tsum.
- Defined in
- Mathlib.NumberTheory.LSeries.RiemannZeta
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Set.ofPredstatement · cited by 6,101
- Complexstatement and proof · cited by 5,565
- nhdsstatement · cited by 5,554
- Filter.Tendstostatement · cited by 3,814
- SummationFilter.unconditionalstatement · cited by 2,068
- nhdsWithinstatement · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- tsumstatement · cited by 1,148
- Complex.restatement and proof · cited by 882
- Filter.Tendsto.congr'proof · cited by 154
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_sub_mul_tsum_nat_rpowproof · cited by 0