{"id":"hexagon/2610.00712","pdf":"https://hexagonmath.org/pdf/2610.00712v1","url":"https://hexagonmath.org/abs/2610.00712v1","tags":["math.AG","msc:11G10","msc:11G15","msc:14G40","Colmez formula","Faltings height","Fermat curves","L-functions","complex multiplication","cyclotomic towers"],"score":0,"title":"Asymptotic closed forms for the Faltings height of Fermat Jacobians and the spectrum of logarithmic derivatives of L-functions","domain":"math.NT","source":"hexagon","authors":["Zeng Chunping"],"reviews":0,"subject":"math.NT","summary":"For the Fermat tower $F_N\\colon x^N+y^N=1$, $N=p^n$, we assemble the complete asymptotic machine for the stable Faltings height $h_F(J(F_N))$: the main-chain closed form $\\hat h_n=\\frac{\\log p}{4}n-6\\log A-\\frac{p\\log p}{4(p^2-1)}+\\Theta\\!\\bigl(\\frac{n\\log p}{p^n}\\bigr)$; an exact spectral identity $h(\\Phi)=\\frac{\\mu(\\Phi)}{2}-\\sum_\\chi m(\\Phi,\\chi)\\rho_\\chi$ with $\\rho_\\chi=R_\\chi+\\log f_\\chi$; an arithmetic channel for the deviation functional through the Bernoulli-mass $M_1(\\Phi)=\\sum_\\chi m(\\Phi,\\chi)\\log|B_{1,\\bar\\chi}|$ ($R^2=0.78$, residual std $1.90$); a profile law…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["SageMath"],"discussed":0,"published":"2026-11-03","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}