Theorems · Theorem · number theory
ArithmeticFunction.LSeries_zeta_eulerProduct_exp_log
∀ {s : ℂ}, 1 < s.re → Complex.exp (∑' (p : Nat.Primes), -Complex.log (1 - ↑↑p ^ (-s))) = LSeries 1 sA variant of the Euler product for the L-series of ζ.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 214 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.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- AddCommMonoidproof · cited by 12,281
- Complexstatement and proof · cited by 5,565
- one_mulproof · cited by 2,841
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- Nat.Primestatement · cited by 2,059
- tsumstatement and proof · cited by 1,148
- Complex.restatement and proof · cited by 882
- Complex.expstatement and proof · cited by 612
- SummationFilterproof · cited by 607
Cited by1
Results whose statement or proof uses this declaration.
- riemannZeta_eulerProduct_exp_logproof · cited by 0