{"id":"hexagon/2610.00651","pdf":"https://hexagonmath.org/pdf/2610.00651v1","url":"https://hexagonmath.org/abs/2610.00651v1","tags":["math.AG","msc:11N37","msc:11M41","power kernel，radical of an integer，CRT conditional law"],"score":0,"title":"Power-Kernel Fluctuations, the Lambert W Subpolynomial Source, and a Local CRT Conditional Law","domain":"math.NT","source":"hexagon","authors":["Zeng Chunping"],"reviews":0,"subject":"math.NT","summary":"For a positive integer $n$ we define the power kernel $d_n = n/\\operatorname{rad}(n)$ and the fluctuation $X_n = \\log d_n$, where $\\operatorname{rad}(n) = \\prod_{p \\mid n} p$. This paper develops three mutually supporting lines around this ``relative fluctuation''. First, the microscopic theory. From the kernel decomposition $n = v_d s$ ($s$ squarefree, $(s,d)=1$, $v_d = d \\operatorname{rad}(d)$) we obtain the exact discrete law $\\mathbb{P}(X_n = \\log d) = \\frac{6}{\\pi^2} \\frac{w(d)}{d \\operatorname{rad}(d)}$, $w(d) := \\prod_{p \\mid d} \\frac{p}{p+1}$, together with a three-branch…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Magma"],"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}