AIProofWatch
← Archive

OpenAI reports: Zero-free regions for zeta and L-functions

OpenAI’s manuscript reports that all Dirichlet L-functions and finite-order Hecke L-functions over Q(√−3) have no zeros with real part greater than 7/8.

You are reading an earlier published revision. Read the current record.

Sources for this record

What was already known

The target is a uniform half-plane bounded away from 1, across conductors and heights. This is distinct from a finite-height computation.

What changed and why it matters

Addresses a substantive research target in the specified setting; this is a reported advance whose correctness and novelty remain subject to mathematical assessment.

The AI contribution

OpenAI attributes the manuscript to an internal frontier model. This entry does not infer the exact human contribution to this individual result from the release-wide description.

Limitations

This is the quasi-Riemann hypothesis, not the full Riemann hypothesis. The principal pole at 1 is allowed. Preprint. AIProofWatch reviewed the source statement and scope, not the full proof, and has not independently run a formal checker.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

Reported theorem in the pinned manuscript. This records the claim, not an independent proof check.

Accessible artifact / proof

Manuscript proof is accessible. Formalization availability alone is not labelled as successful formal verification.

Correction and publication history

2026-10-11 · amendment

Editorial importance reassessment: rate the scoped impact if correct independently from verification. The claim, limitations, sources, and verification evidence are unchanged.

Read this published revision