Theorems · Theorem · number theory
DirichletCharacter.modOne_eq_one
∀ {R : Type u_1} [inst : CommMonoidWithZero R] {χ : DirichletCharacter R 1}, (fun x => χ ↑x) = 1The Dirichlet character mod 1 corresponds to the constant function 1.
- Defined in
- Mathlib.NumberTheory.LSeries.Dirichlet
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- ZModstatement · cited by 1,024
- CommMonoidWithZerostatement and proof · cited by 913
- DirichletCharacterstatement and proof · cited by 161
- Pi.one_applyproof · cited by 22
- MulChar.one_applyproof · cited by 10
- isUnit_of_subsingletonproof · cited by 9
- DirichletCharacter.level_oneproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- LSeries.abscissaOfAbsConv_oneproof · cited by 3
- LSeriesSummable_one_iffproof · cited by 2
- ArithmeticFunction.LSeries_zeta_eulerProduct_exp_logproof · cited by 1
- DirichletCharacter.LSeries_modOne_eqproof · cited by 1