Theorems · Theorem · number theory
DirichletCharacter.LSeries_ne_zero_of_one_lt_re
∀ {N : ℕ} (χ : DirichletCharacter ℂ N) {s : ℂ}, 1 < s.re → LSeries (fun n => χ ↑n) s ≠ 0The L-series of a Dirichlet character does not vanish on the right half-plane re s > 1.
- Defined in
- Mathlib.NumberTheory.LSeries.Dirichlet
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- MulZeroClass.zero_mulproof · cited by 1,625
- ZModstatement · cited by 1,024
- Complex.restatement and proof · cited by 882
- DirichletCharacterstatement and proof · cited by 161
- LSeriesstatement and proof · cited by 77
- ArithmeticFunction.moebiusproof · cited by 45
- DirichletCharacter.LSeries.mul_mu_eq_oneproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- DirichletCharacter.LFunction_ne_zero_of_one_le_reproof · cited by 5
- DirichletCharacter.LSeries_twist_vonMangoldt_eqproof · cited by 2