Theorems · Theorem · number theory
riemannZeta_ne_zero_of_one_lt_re
∀ {s : ℂ}, 1 < s.re → riemannZeta s ≠ 0The Riemann Zeta Function does not vanish on the half-plane re s > 1.
- Defined in
- Mathlib.NumberTheory.LSeries.Dirichlet
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 307 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Complex.restatement and proof · cited by 882
- riemannZetastatement · cited by 85
- LSeries_one_eq_riemannZetaproof · cited by 6
- LSeries_one_ne_zero_of_one_lt_reproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- EisensteinSeries.q_expansion_riemannZetaproof · cited by 1