Independent rewrites support OpenAI's quasi-Riemann and Landau–Siegel claims

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Stable ID

math-quasi-riemann-landau-siegel-2026

Revision

math-quasi-riemann-landau-siegel-2026.v2

Field

Mathematics · Analytic number theory and L-functions

Evidence

Tier 1 · Peer reviewed: No

Record state

Provisional · Independently unpacked provisional proofs

Last checked

2026-10-22

AI role

OpenAI attributes the originating manuscripts to an internal frontier model with human assistance. Banks reports using Claude to expand and revise the proof, work out explicit constants, check arguments and references, and prepare text and figures. He states that he checked every line and takes full responsibility. Kerr credits ChatGPT with assistance in the mathematical development and preparation of his paper. These are independently authored, AI-assisted expositions; the authors remain responsible for their arguments.

Record details

Problem or result

Quasi-Riemann hypothesis for Dirichlet L-functions and exclusion of Landau–Siegel zeros

Authors

OpenAI; independent proofs by William D. Banks and Bryce Kerr

Institutions

OpenAI; University of Missouri (William D. Banks); School of Science, UNSW Canberra (Bryce Kerr). Banks also acknowledges support from the Max Planck Institute for Mathematics in Bonn.

Result date

OpenAI manuscripts dated October 1 and 5; independent preprints submitted October 11 and 15; specialist assessment published October 19, 2026

Why it matters

A fixed zero-free half-plane would materially strengthen control of primes in arithmetic progressions and settle the Landau–Siegel exceptional-zero problem. Independently authored, AI-assisted expositions make the argument more inspectable, while their authors retain responsibility for checking it.

Limits

None of the papers is peer reviewed. Specialists quoted by Quanta largely judged the 11/12 argument correct, but Peter Sarnak declined to call it a theorem until every detail is checked, and experts set aside a separate stronger 7/8 manuscript because its exposition was too difficult to audit. The tracker therefore does not mark either claim as an unqualified proved theorem.

Sources

1. Primary: OpenAI quasi-Riemann hypothesis manuscript
2. Primary: OpenAI Landau–Siegel zero exclusion manuscript
3. Independent proof: Banks direct proof with explicit constants
4. Independent proof: Kerr simplified Landau–Siegel proof
5. Independent specialist assessment: Quanta assessment of the quasi-Riemann proof

Correction and revision history

1. 2026-10-22 — Added after primary-source, scope, status, AI-role and limitation review.
2. 2026-10-22 — Corrected the scope of Banks's Claude assistance, added Kerr's ChatGPT disclosure and verified both university affiliations. Proof claims, evidence tier, peer-review state and provisional status are unchanged.

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