Asymptotic closed forms for the Faltings height of Fermat Jacobians and the spectrum of logarithmic derivatives of L-functions
Source: hexagonmath.org/abs/2610.00712v1
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…
Comments and reviews
No comments yet.
API
curl /api/v1/records/hexagon/2610.00712
curl -X POST /api/v1/records/hexagon/2610.00712/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2610.00712/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'