OpenAI paper extends zeta zero-free region to Re(s)>7/8, a fixed gap toward Riemann hypothesis
PTenigma · x · 2026-10-08
A breakdown of OpenAI's new Riemann hypothesis paper: classical zero-free regions only approached Re(s)=1 asymptotically, leaving zeros possible at Re(s)=0.99 at enormous heights. The new result claims a fixed gap—ζ(s)≠0 for Re(s)>7/8—using the Möbius expansion 1/ζ(s)=∑μ(n)/n^s for Re(s)>1 and strong cancellation of the Möbius function's signs. The author also describes using an LLM to progressively explain the many branches of math involved.
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