The mixing conjecture under GRH
Number Theory
2025-11-24 v2
Abstract
We prove the Mixing Conjecture of Michel--Venkatesh for the class group action on Heegner points of large discriminant on compact arithmetic surfaces attached to maximal orders in rational quaternion algebras. The proof is conditional on the Generalized Riemann Hypothesis, and when the division algebra is indefinite we furthermore assume the Ramanujan conjecture. Our methods, which provide an effective rate, are based on the spectral theory of automorphic forms and their -functions, as well as techniques in classical analytic number theory.
Keywords
Cite
@article{arxiv.2212.06280,
title = {The mixing conjecture under GRH},
author = {Valentin Blomer and Farrell Brumley and Ilya Khayutin},
journal= {arXiv preprint arXiv:2212.06280},
year = {2025}
}
Comments
59 pages, corrections taking into account referee reports, treatment of Eisenstein series simplified, to appear in Annales Scientifiques de l'ENS