{"id":"hexagon/2610.00706","pdf":"https://hexagonmath.org/pdf/2610.00706v1","url":"https://hexagonmath.org/abs/2610.00706v1","tags":["msc:11J86","msc:11J61","Baker's method","Yu's theorem","interpolation determinants","linear forms in p-adic logarithms"],"score":0,"title":"A kit for linear forms in three $p$-adic logarithms","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["David Niedbala Giraudin"],"reviews":0,"subject":"math.NT","summary":"We transpose to the $p$-adic case the kit of Mignotte and Voutier for linear forms in three logarithms. The new tool is a lower bound for the $p$-adic valuation of interpolation determinants with no factorial loss: it is obtained by expanding the powers $\\theta^{\\ell z}$ as binomial series in $\\theta-1$, and then transporting an order of vanishing that we compute optimally for generic points, by means of the initial forms of the space of exponential polynomials involved. It holds for every prime $p$. Combined with a rearrangement bound for the spread of the exponents and with Gouillon's zero…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}