A Problem on Sums of Two Squares

Enrico Bombieri, Jean Bourgain

Type: Article

Publication Date: 2014-03-18

Citations: 70

DOI: https://doi.org/10.1093/imrn/rnu005

Abstract

Krishnapur et al. [15] studied the length of the fluctuations of nodal lengths of random Laplace eigenfunctions on the standard 2-torus. A key step in the paper is a nontrivial bound for the sixth-order correlation of the integer solutions of the equation m=x2+y2. This is a problem about a certain diophantine equation, studied here in depth using a variety of methods.

Locations

International Mathematics Research Notices - View - PDF

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