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On Landau--Siegel zeros

Primarily human-written textHuman understanding: all partsmath.NT — Number Theory

Contributed by Ben Green

Version 2 / Oct 17, 2026 / CC BY 4.0

Abstract

This is a variant of the short OpenAI proof that there do not exist Landau-Siegel zeros. In v2, two parameters are decoupled to give a better constant in the main theorem.

Provenance statement

The mathematical arguments are all due to ChatGPT, prompted in various ways by the author. The text is entirely human-written.

References

  1. W. D. Banks, On the OpenAI proof that Landau--Siegel zeros do not exist , arXiv:2610.15483.arXiv
  2. B. Kerr, A simpler proof that there are no Landau--Siegel zeros , arXiv:2610.21099.arXiv
  3. OpenAI, Uniform exclusion of Landau--Siegel zeros , OpenAI Math Release preprint (2026). Available online (https://github.com/openai/math/blob/main/preprints/Uniform-exclusion-of-Landau-Siegel-zeros-October-1-2026/paper.pdf).link

Version history

  1. v1Submitted by Ben GreenInitial depositSupersededOct 17, 2026
  2. v2Submitted by Ben GreenSubmitted as a new versionCurrentOct 18, 2026