Theorems · Theorem · number theory
DirichletCharacter.LFunction_ne_zero_of_re_eq_one
∀ {N : ℕ} (χ : DirichletCharacter ℂ N) [inst : NeZero N] {s : ℂ},
s.re = 1 → χ ≠ 1 ∨ s ≠ 1 → DirichletCharacter.LFunction χ s ≠ 0If χ is a Dirichlet character, then L(χ, s) does not vanish when s.re = 1
except when χ is trivial and s = 1 (then L(χ, s) has a simple pole at s = 1).
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 316 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Complex.ofReal_oneproof · cited by 43
Cited by1
Results whose statement or proof uses this declaration.
- DirichletCharacter.LFunction_ne_zero_of_one_le_reproof · cited by 5