Quantitative strong approximation for quaternary quadratic forms
Number Theory
2025-01-29 v1
Abstract
The purpose of this article is twofold. On the one hand, we prove asymptotic formulas for the quantitative distribution of rational points on any smooth non-split projective quadratic surface. We obtain the optimal error term for the real place. On the other hand, we also study the growth of integral points on the three-dimensional punctured affine cone, as a quantitative version of strong approximation with Brauer--Manin obstruction for this quasi-affine variety.
Cite
@article{arxiv.2501.16766,
title = {Quantitative strong approximation for quaternary quadratic forms},
author = {Zhizhong Huang and Damaris Schindler and Alec Shute},
journal= {arXiv preprint arXiv:2501.16766},
year = {2025}
}