On a generalization of a theorem of Popov
Number Theory
2019-10-31 v1
Abstract
In this paper, we obtain sharp estimates for the number of lattice points under and near the dilation of a general parabola, the former generalizing an old result of Popov. We apply Vaaler's lemma and the Erd\H{o}s-Turan inequality to reduce the two underlying counting problems to mean values of a certain quadratic exponential sums, whose treatment is subject to classical analytic techniques.
Keywords
Cite
@article{arxiv.1910.13715,
title = {On a generalization of a theorem of Popov},
author = {Jing-Jing Huang and Huixi Li},
journal= {arXiv preprint arXiv:1910.13715},
year = {2019}
}