OpenAI research collection · 3 manuscripts · Source checked 2026-10-19
Proves that every Dirichlet L-function, including \zeta(s), is zero-free in \Re s> 7/8, resolving the quasi-Riemann hypothesis. The same half-plane is zero-free for every finite-order Hecke L-function over \mathbb Q(\sqrt{-3}). A companion gives a different proof of the zero-free half-plane \Re s> 11/12.
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We prove that all finite-order Hecke L-functions over \mathbb Q(\sqrt{-3}) and all Dirichlet L-functions are zero-free in the half-plane \Re s> 7/8, with the principal pole at s = 1 allowed. In particular, the Riemann zeta function is zero-free in this half-plane, proving the quasi-Riemann hypothesis.
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We establish the quasi-Riemann hypothesis by proving that every Dirichlet L-function, including Riemann's zeta function, has no zeros in the half-plane \mathop{Re}\nolimits s> 11/12. More generally, we prove the same zero-free half-plane for every finite-order Hecke L-function over K=\mathbb Q(\sqrt{-3}). In particular, this…
We establish the quasi-Riemann hypothesis by proving that every Dirichlet L-function, including Riemann's zeta function, has no zeros in the half-plane \mathop{Re}\nolimits s> 11/12. More generally, we prove the same zero-free half-plane for every finite-order Hecke L-function over K=\mathbb Q(\sqrt{-3}). In particular, this rules out the existence of Landau–Siegel zeros.
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We prove the uniform exclusion of Landau–Siegel zeros. There is an absolute constant c > 0 such that every real zero β∈(0,1) of every primitive nonprincipal real Dirichlet L-function of conductor q ≥ 3 satisfies (1-β)log q≥ c.
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