Lattice points on small arcs

2021/07/21 by Kristina Oganesyan, Oganesyan, Kristina
Mathematics · #11L05 (Secondary) #11P21 (Primary) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2107.09991

openalex publication_date 2021/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for any α∈ (1/2,1) the number of lattice points belonging to an arc of length R^α of the circle of radius R centered at the origin is not uniformly bounded in R, which disproves the corresponding conjecture of Cilleruelo and Granville. We also give certain generalizations of this fact and estimates for the L₄-norm of Gauss sums.

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