Some remarks on Heath-Brown's theorem on quadratic forms
Number Theory
2021-04-27 v1 Analysis of PDEs
Abstract
In his paper from 1996 on quadratic forms Heath-Brown developed a version of circle method to count points in the intersection of an unbounded quadric with a lattice of short period, if each point is given a weight. The weight function is assumed to be -smooth and to vanish near the singularity of the quadric. In out work we allow the weight function to be finitely smooth and not vanish near the singularity, and we give also an explicit dependence on the weight function.
Keywords
Cite
@article{arxiv.2104.11794,
title = {Some remarks on Heath-Brown's theorem on quadratic forms},
author = {Andrey Dymov and Sergei Kuksin and Alberto Maiocchi and Sergei Vladuts},
journal= {arXiv preprint arXiv:2104.11794},
year = {2021}
}