English

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.

Keywords

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}
}
R2 v1 2026-06-28T21:21:32.789Z