Theorems · Theorem · number theory
DirichletCharacter.LSeriesSummable_of_one_lt_re
∀ {N : ℕ} (χ : DirichletCharacter ℂ N) {s : ℂ}, 1 < s.re → LSeriesSummable (fun n => χ ↑n) sThe L-series of a Dirichlet character converges absolutely at s if re s > 1.
- Defined in
- Mathlib.NumberTheory.LSeries.Dirichlet
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- ZModstatement · cited by 1,024
- Complex.restatement and proof · cited by 882
- DirichletCharacterstatement and proof · cited by 161
- LSeriesSummablestatement · cited by 59
- DirichletCharacter.norm_le_oneproof · cited by 7
- LSeriesSummable_of_bounded_of_one_lt_reproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- DirichletCharacter.LSeriesSummable_iffproof · cited by 3
- DirichletCharacter.LSeries.mul_mu_eq_oneproof · cited by 1