Theorems · Theorem · number theory
DirichletCharacter.Even.LFunction_neg_two_mul_nat_add_one
∀ {N : ℕ} [inst : NeZero N] {χ : DirichletCharacter ℂ N},
χ.Even → ∀ (n : ℕ), DirichletCharacter.LFunction χ (-(2 * (↑n + 1))) = 0The L-function of an even Dirichlet character vanishes at strictly negative even integers.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 307 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- DirichletCharacterstatement and proof · cited by 161
- DirichletCharacter.LFunctionstatement · cited by 23
- DirichletCharacter.Evenstatement and proof · cited by 13
- DirichletCharacter.Even.to_funproof · cited by 3
- ZMod.LFunction_neg_two_mul_nat_add_oneproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- DirichletCharacter.Even.LFunction_neg_two_mul_natproof · cited by 0