Theorems · Theorem · number theory
HurwitzZeta.hasSum_hurwitzZeta_of_one_lt_re
∀ {a : ℝ}, a ∈ Set.Icc 0 1 → ∀ {s : ℂ}, 1 < s.re → HasSum (fun n => 1 / (↑n + ↑a) ^ s) (HurwitzZeta.hurwitzZeta (↑a) s)Formula for hurwitzZeta s as a Dirichlet series in the convergence range. We
restrict to a ∈ Icc 0 1 to simplify the statement.
- Defined in
- Mathlib.NumberTheory.LSeries.HurwitzZeta
- Cited by
- 1 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- AddCommMonoidproof · cited by 12,281
- Complexstatement and proof · cited by 5,565
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Set.Iccstatement and proof · cited by 1,702
- Complex.ofRealstatement and proof · cited by 1,654
- Complex.restatement and proof · cited by 882
- SummationFilterproof · cited by 607
- HasSumstatement and proof · cited by 518
- AddSubgroup.zmultiplesstatement · cited by 493
Cited by1
Results whose statement or proof uses this declaration.
- ZMod.LFunction_eq_LSeriesproof · cited by 1