{"id":"hexagon/2610.00274","pdf":"https://hexagonmath.org/pdf/2610.00274v1","url":"https://hexagonmath.org/abs/2610.00274v1","tags":["math.NT","msc:20G05","msc:20C15","msc:22C05","msc:41A05","msc:11R45","Abel resolvents","Chebotarev density theorem","GL2","PGL2"],"score":0,"title":"Finite Projective Source Geometry for GL2: Abel Resolvents and Central-Jet Degree Laws","domain":"math.RT","origin":"ai-generated","source":"hexagon","authors":["Shawn Schafer"],"reviews":0,"subject":"math.RT","summary":"Starting from the two trace functions p1 = Tr(A) and p2 = Tr(A^2) for semisimple A in GL2(C), we develop the associated projective source geometry. The coordinate y = t^2/d - 1 identifies the adjoint character, and normalized Haar measure on a specified closed subgroup H of SO(3) pushes forward to a probability measure nu_H. We describe this measure through harmonic multiplicities, moments, and its Stieltjes transform, and prove that it determines H up to conjugacy within the closed-subgroup class of SO(3). A positive Abel kernel resums the projective character tower and gives a resolvent…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","ChatGPT"],"discussed":0,"published":"2026-10-15","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}