Bryce Kerr gives 6-page simpler proof that Landau–Siegel zeros don't exist
aran_nayebi · x · 2026-10-18
Bryce Kerr posted a 6-page paper simplifying OpenAI's recent proof that Landau–Siegel zeros do not exist.
- Theorem: there is an absolute constant c > 0 such that for every primitive nonprincipal real Dirichlet character χ(n) = (q/n), every real zero β ∈ (0,1) of L(s,χ) satisfies (1−β)log|q| ≥ c.
- Method: keeps OpenAI's idea of polynomials vanishing modulo many primes at linear forms, but replaces interpolation and determinant analysis with the pigeonhole principle to find a bounded-degree polynomial f; a classical result of Masser then contradicts the degree bound.
- Bill Banks uploaded an exposition of the proof, and commentators call it a possible "Proof from the Book."
More from AGI Musings
- Super-Worms Warning: AI-Powered Self-Propagating Malware and a Fragmenting Internet — JensHonack · 2026-10-23
- Wolfram Opens Rule 30 Prizes to AIs: $30,000 for Three Open Problems — cephaloform · 2026-10-23
- Mathematicians and Biomedical Researchers React to AI in Strikingly Different Ways — manorlaboratory · 2026-10-23
- Stanford and Databricks use AI agents to reproduce medical findings and test analytical robustness — ChengleiSi · 2026-10-23
- ISMS Fellow Avi Goldfarb: AI disruption raises returns to exploring research directions — avicgoldfarb · 2026-10-23
- signull on AI-found PHP exploits: economic liability is the forcing function legacy software needs — signulll · 2026-10-23