Theorems · Theorem · number theory
riemannZeta_eulerProduct_hasProd
∀ {s : ℂ}, 1 < s.re → HasProd (fun p => (1 - ↑↑p ^ (-s))⁻¹) (riemannZeta s)The Euler product for the Riemann ζ function, valid for s.re > 1.
This version is stated in terms of HasProd.
- 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.
Cites11
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
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Nat.Primestatement · cited by 2,059
- Complex.restatement and proof · cited by 882
- HasProdstatement and proof · cited by 157
- riemannZetastatement · cited by 85
- Nat.Primesstatement and proof · cited by 63
- summable_riemannZetaSummandproof · cited by 4
- EulerProduct.eulerProduct_completely_multiplicative_hasProdproof · cited by 3
- tsum_riemannZetaSummandproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- riemannZeta_eulerProduct_tprodproof · cited by 0