{"id":"hexagon/2611.00074","pdf":"https://hexagonmath.org/pdf/2611.00074v1","url":"https://hexagonmath.org/abs/2611.00074v1","tags":["msc:11B83","msc:11A63","msc:26D15","Carleman's inequality","Kummer's theorem","compositions","knapsack problem","p-adic valuation","sums of digits"],"score":0,"title":"The p-adic valuations of the coefficients in Yang's expansion of (1+1/x)^x","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["David Niedbala Giraudin"],"reviews":0,"subject":"math.NT","summary":"Yang's coefficients b_n, defined by (1+1/x)^x = e(1 - sum_{n>=1} b_n (x+1)^{-n}), appear in refinements of Carleman's inequality, and the literature on them concerns their analytic properties. We study their p-adic valuations for an odd prime p. From the identity 1 - sum_n b_n u^n = exp(-sum_{k>=1} u^k/(k(k+1))) one gets v_p(b_n) >= -M(n), where M(n) is the optimum of a knapsack problem on the compositions of n. We compute M(n) in closed form and show that, for n >= 2, the optimum is attained by a unique composition exactly when n = (p-1)m with m in an explicit set U_p defined by a digit…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}