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The quasi-Riemann hypothesis
Proves that every Dirichlet L-function, including , is zero-free in , resolving the quasi-Riemann hypothesis. The same half-plane is zero-free for every finite-order Hecke L-function over . A companion gives a different proof of the zero-free half-plane .
Manuscripts in this family · 3
The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane
Sep 30, 2026·paper.pdfLean
We prove that all finite-order Hecke L-functions over and all Dirichlet L-functions are zero-free in the half-plane , 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.
The Quasi-Riemann Hypothesis (alternate 11/12 proof)
Oct 5, 2026·paper2.pdf
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 . More generally, we prove the same zero-free half-plane for every finite-order Hecke L-function over . In particular, this rules out the existence of Landau–Siegel zeros.
Uniform exclusion of Landau–Siegel zeros
Oct 1, 2026·paper.pdfLean
We prove the uniform exclusion of Landau–Siegel zeros. There is an absolute constant c > 0 such that every real zero of every primitive nonprincipal real Dirichlet L-function of conductor q ≥ 3 satisfies .