Kominers lifts the Landau–Siegel determinant argument to finite Galois extensions in new note
soumitrashukla9 · x · 2026-10-20
Scott Duke Kominers posted a short note, Small algebraic integers and Frobenius prime sums, showing that the streamlined determinant argument from recent Landau–Siegel zero exclusion proofs (Green's distillation of OpenAI's proof, in Barreto's Wronskian form) lifts directly to finite Galois extensions of Q. He bounds weighted Frobenius prime sums via a determinant built from small algebraic integers, yielding a uniform height bound, a weighted Chebotarev estimate per fixed field, and — specializing to quadratic fields — uniform Landau–Siegel zero exclusion with an effective lower bound on (1−β)log q. The note credits GPT-6 Astra for assistance during exploration and Claude Opus 5.5 for identifying earlier precedents (Selberg, Dobrowolski, Cantor–Straus, etc.).
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