Theorems · Theorem · number theory
DirichletCharacter.LSeries_eulerProduct_exp_log
∀ {N : ℕ} (χ : DirichletCharacter ℂ N) {s : ℂ},
1 < s.re → Complex.exp (∑' (p : Nat.Primes), -Complex.log (1 - χ ↑↑p * ↑↑p ^ (-s))) = LSeries (fun n => χ ↑n) sA variant of the Euler product for Dirichlet L-series.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- 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
- map_zeroproof · cited by 1,614
- tsumstatement and proof · cited by 1,148
- eq_or_neproof · cited by 1,117
- ZModstatement · cited by 1,024
- Complex.restatement and proof · cited by 882
- div_eq_mul_invproof · cited by 715
- MonoidWithZeroHomproof · cited by 704
Cited by3
Results whose statement or proof uses this declaration.
- DirichletCharacter.norm_LSeries_product_ge_oneproof · cited by 1
- DirichletCharacter.LSeries_eq_exp_LSeriesproof · cited by 1
- ArithmeticFunction.LSeries_zeta_eulerProduct_exp_logproof · cited by 1