On a generalization of a theorem of Popov

2019/10/30 by Jing-Jing Huang, Huang, Jing-Jing, Huixi Li +1
Mathematics · #11J25 #11P21 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1910.13715

openalex publication_date 2019/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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