Theorems · Theorem · number theory
ZMod.LFunction_neg_two_mul_nat_sub_one
∀ {N : ℕ} [inst : NeZero N] {Φ : ZMod N → ℂ}, Function.Odd Φ → ∀ (n : ℕ), ZMod.LFunction Φ (-(2 * ↑n) - 1) = 0The L-function of an odd function vanishes at negative odd integers.
- Defined in
- Mathlib.NumberTheory.LSeries.ZMod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 306 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Complexstatement and proof · cited by 5,565
- Finset.univproof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.mul_zeroproof · cited by 2,091
- ZModstatement and proof · cited by 1,024
- Finset.sum_const_zeroproof · cited by 219
- Function.Oddstatement and proof · cited by 38
- ZMod.toAddCircleproof · cited by 32
- ZMod.LFunctionstatement · cited by 16
- ZMod.LFunction.congr_simpproof · cited by 2
- ZMod.LFunction_def_oddproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- DirichletCharacter.Odd.LFunction_neg_two_mul_nat_sub_oneproof · cited by 0