{"id":"palomar/PALOMAR-2026-09-14-000011","url":"https://github.com/abhisaha-git/fourier-jacobi-core-evaluation/tree/fb2b788d6271dd6228044b2c4e9e47c891a16762","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-14-000011-v1.json","repo":"https://github.com/abhisaha-git/fourier-jacobi-core-evaluation","tags":["math.NT","math.RT","msc:11F70","msc:11F85","number-theory","representation-theory","harmonic-analysis","p-adic"],"score":0,"title":"Explicit Fourier–Jacobi Haar-core evaluation and Abel limits","trust":"high","domain":"math.NT","source":"palomar","authors":["Abhishek Saha"],"reviews":0,"subject":"math.NT","summary":"For a nonarchimedean local field with residue cardinality q > 2, this development evaluates a sum of three normalized Haar integrals of an explicit eight-term Weyl kernel defined from valuations of entries and two-by-two minors of a concrete 4 by 4 matrix. It proves measurability and Bochner integrability on the natural damped range, an explicit rational evaluation in the undamped interior, principal Abel convergence, and the whole signed special Abel limit at delta = plus or minus q^(-1/2). The Satake parameters are unitary and avoid the stated Weyl walls; the special quotient also excludes…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-14","reactions":{},"formalized":true,"formalizes":[{"title":"An explicit refined Gan–Gross–Prasad identity for Fourier–Jacobi periods of degree 2 Siegel cusp forms","identifier":"https://arxiv.org/abs/2608.26007","relationship":"adapts"},{"title":"Expanded Section 2 and corrected core-evaluation brief","identifier":"PROVENANCE.md","relationship":"adapts"}]}