Theorems · Theorem · number theory
DirichletCharacter.mem_conductorSet_iff_conductor_dvd
∀ {R : Type u_1} [inst : CommMonoidWithZero R] {n : ℕ} (χ : DirichletCharacter R n) {d : ℕ} [NeZero n],
d ∣ n → (d ∈ χ.conductorSet ↔ χ.conductor ∣ d)A divisor d of n belongs to the conductor set of χ if and only if the conductor of χ
divides d.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZeroNeZero
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.
- Setstatement · cited by 53,352
- CommMonoidWithZerostatement and proof · cited by 913
- DirichletCharacterstatement and proof · cited by 161
- DirichletCharacter.conductorstatement and proof · cited by 29
- DirichletCharacter.conductorSetstatement · cited by 8
- DirichletCharacter.factorsThrough_conductorproof · cited by 4
- DirichletCharacter.conductor_dvd_of_mem_conductorSetproof · cited by 2
- DirichletCharacter.FactorsThrough.monoproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- DirichletCharacter.conductor_zpow_dvdproof · cited by 2
- DirichletCharacter.conductor_mul_dvd_lcm_conductorproof · cited by 0