{"id":"hexagon/2610.00468","pdf":"https://hexagonmath.org/pdf/2610.00468v1","url":"https://hexagonmath.org/abs/2610.00468v1","tags":["msc:11R09","msc:11R32","msc:11N13","Jacobi polynomial","Kaneko--Zagier polynomial","Legendre polynomial"],"score":0,"title":"Arithmetic of Jacobi polynomials","domain":"math.GM","origin":"ai-generated","source":"hexagon","authors":["Khai Hoan Nguyen Dang"],"reviews":0,"subject":"math.GM","summary":"We study the arithmetic of Jacobi polynomials. As applications, we prove the Mahlburg--Ono conjecture on the irreducibility and Galois groups of the four Kaneko--Zagier families, and the Cullinan--Hajir conjecture on the Galois groups of Legendre polynomials. Other applications concern common zeros of Jacobi polynomials, harmonic functions on cones, and hyperelliptic Jacobians.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Codex"],"discussed":0,"published":"2026-10-22","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}