{"id":"hexagon/2610.00451","pdf":"https://hexagonmath.org/pdf/2610.00451v1","url":"https://hexagonmath.org/abs/2610.00451v1","tags":["msc:11M20","msc:11R44","msc:11R45","msc:11N13","msc:11R04","Chebotarev density theorem","Frobenius congruence","Galois extension","Geometry of numbers","Landau–Siegel zero"],"score":0,"title":"Small algebraic integers and Frobenius prime sums","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Scott Kominers"],"reviews":0,"subject":"math.NT","summary":"The determinant argument in recent proofs of Landau–Siegel zero exclusion compares the size of a nonzero integer with its divisibility by inert primes. We observe that the same comparison applies to every Frobenius class in a finite Galois extension of $\\mathbb{Q}$, bounding its weighted prime count in terms of the supply of small algebraic integers. For each fixed field, the resulting height bound implies a weighted Chebotarev theorem whose only analytic inputs are the elementary Chebyshev and Mertens estimates. In the quadratic case there are only two Frobenius classes, so the lower bound…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Claude Opus","Poe"],"discussed":0,"published":"2026-10-22","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}