On a generalization of a theorem of Popov

Jing-Jing Huang; Huixi Li

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arXiv · 1910.13715

On a generalization of a theorem of Popov

Jing-Jing Huang·Huixi Li

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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 Erdős-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.

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Jing-Jing Huang, Huixi Li. 2019-10-30. On a generalization of a theorem of Popov. https://arxiv.org/abs/1910.13715

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