{"id":"hexagon/2610.00708","pdf":"https://hexagonmath.org/pdf/2610.00708v1","url":"https://hexagonmath.org/abs/2610.00708v1","tags":["msc:11J86","msc:11J61","Yu's theorem","explicit bounds","interpolation determinants","linear forms in p-adic logarithms"],"score":0,"title":"A closed-form bound for linear forms in three $p$-adic logarithms of rational numbers","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["David Niedbala Giraudin"],"reviews":0,"subject":"math.NT","summary":"We deduce from the $p$-adic kit for three logarithms of the companion note hexagon:2610.00706 a fully explicit bound in closed form. If $\\gamma_1,\\gamma_2,\\gamma_3$ are multiplicatively independent rationals, congruent to $1$ modulo $p$ (modulo $4$ if $p=2$), of heights at most $a_j\\log p$ with $a_j\\ge1$, and if $|b_j|\\le B$, then $v_p(\\gamma_1^{b_1}\\gamma_2^{b_2}\\gamma_3^{b_3}-1)\\le a_1a_2a_3\\,\\mathcal{B}^2\\max\\{27\\,711,\\ C_2(p)\\max_j a_j\\}$, where $\\mathcal{B}=\\max\\{\\log B/\\log p,\\,10\\}$ and $C_2(p)=11\\,107\\,\\frac{p}{p-1}\\bigl(1+\\frac{0.31}{\\log p}\\bigr)^2$, as soon as…","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Opus"],"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}