Zeta zeros on the critical line

Scope and what remains

Not RH. Keep simple versus distinct zeros and the multiplicity denominator explicit. Superseded 1/2 and 3/4 theorems remain in source history; do not mistake them for the current headline.

Contributors

An unreleased research Claude supplied the argument after prompting by Jarred Sumner. Levent Alpöge and Ralph Furman rederived and wrote the mathematics; Eric Easley orchestrated formalization. Earlier human analytic inputs retain attribution.

AI systems: Claude

Sources

More on Riemann hypothesis

October 2026 1

Oct 6, 2026

New proofNumber theoryopenai/math #003

Quasi-Riemann hypothesis

Proves that every Dirichlet L-function, including $\zeta(s)$ , is zero-free in $\Re s\gt 7/8$ , 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 $\Re s\gt 11/12$ .

Unreleased OpenAI modelProblem page →

LFCR