Theorems · Theorem · number theory
DirichletCharacter.Odd.LFunction_neg_two_mul_nat_sub_one
∀ {N : ℕ} [inst : NeZero N] {χ : DirichletCharacter ℂ N},
χ.Odd → ∀ (n : ℕ), DirichletCharacter.LFunction χ (-(2 * ↑n) - 1) = 0The L-function of an odd Dirichlet character vanishes at negative odd integers.
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- Foundations
- Depth 307 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
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- Complexstatement and proof · cited by 5,565
- DirichletCharacterstatement and proof · cited by 161
- DirichletCharacter.LFunctionstatement · cited by 23
- DirichletCharacter.Oddstatement and proof · cited by 11
- DirichletCharacter.Odd.to_funproof · cited by 3
- ZMod.LFunction_neg_two_mul_nat_sub_oneproof · cited by 1
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