Theorems · Theorem · number theory
DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow
∀ {N : ℕ} (χ : DirichletCharacter ℂ N) {s : ℂ}, 1 < s.re → Summable fun p => -Complex.log (1 - χ ↑↑p * ↑↑p ^ (-s))The logarithms of the Euler factors of a Dirichlet L-series form a summable sequence.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
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- SummationFilter.unconditionalstatement · cited by 2,068
- Nat.Primestatement · cited by 2,059
- ZModstatement · cited by 1,024
- Complex.restatement and proof · cited by 882
- Summablestatement · cited by 778
- norm_nonnegproof · cited by 725
- Nat.cast_nonneg'proof · cited by 245
- Complex.logstatement · cited by 187
Cited by1
Results whose statement or proof uses this declaration.
- DirichletCharacter.norm_LSeries_product_ge_oneproof · cited by 1