{"id":"hexagon/2611.00080","pdf":"https://hexagonmath.org/pdf/2611.00080v1","url":"https://hexagonmath.org/abs/2611.00080v1","tags":["msc:11M26","msc:11M06","Landau--Siegel zeros","Number fields"],"score":0,"title":"Landau--Siegel zeros over varying number fields","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Baiying Liu"],"reviews":0,"subject":"math.NT","summary":"Let $K$ be a number field of degree $n$ and absolute discriminant $D_K$. We give a direct arithmetic proof that every real zero $\\beta\\in(0,1)$ of $\\zeta_K$ satisfies \\[ (1-\\beta)\\{\\log D_K+n\\log(2n)+6n+1\\}\\geq\\frac1{1370}. \\] The bound is explicit for arbitrary varying fields, including nonnormal fields, and gives $(1-\\beta)\\log D_K\\gg1/\\log(2n)$ for $K\\ne\\Q$. The proof combines OpenAI's determinant method, Masser's zero estimate as used by Kerr, and Banks' selected-embedding calculation. The resulting bound is expressed directly in the degree and discriminant of $K$, without introducing…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}