Effective equidistribution in rank 2 homogeneous spaces and values of quadratic forms
Dynamical Systems
2025-07-22 v2 Number Theory
Abstract
We establish effective equidistribution theorems, with a polynomial error rate, for orbits of unipotent subgroups in quotients of quasi-split, almost simple Linear algebraic groups of absolute rank 2. As an application, inspired by the results of Eskin, Margulis and Mozes, we establish quantitative results regarding the distribution of values of an indefinite ternary quadratic form at integer points, giving in particular an effective and quantitative proof of the Oppenheim Conjecture.
Keywords
Cite
@article{arxiv.2503.21064,
title = {Effective equidistribution in rank 2 homogeneous spaces and values of quadratic forms},
author = {Elon Lindenstrauss and Amir Mohammadi and Zhiren Wang and Lei Yang},
journal= {arXiv preprint arXiv:2503.21064},
year = {2025}
}
Comments
Corrected a few typos, including in the statement of Theorem 2.3, and additional small changes