Lattice points on small arcs

Kristina Oganesyan

Lattice points on small arcs

Number Theory 2021-08-24 v2 Classical Analysis and ODEs

Authors: Kristina Oganesyan

Abstract

We show that for any $\alpha\in (1/2,1)$ the number of lattice points belonging to an arc of length $R^{\alpha}$ 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 $L_4$ -norm of Gauss sums.

Keywords

lattice theory

Cite

@article{arxiv.2107.09991,
  title  = {Lattice points on small arcs},
  author = {Kristina Oganesyan},
  journal= {arXiv preprint arXiv:2107.09991},
  year   = {2021}
}

Comments

The paper is withdrawn because of a mistake in Lemma 2

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