On Linnik's conjecture: sums of squares and microsquares
Number Theory
2022-02-14 v1
Abstract
We show that almost all natural numbers n not divisible by 4, and not congruent to 7 modulo 8, are represented as the sum of three squares, one of which is the square of an integer no larger than (log n)^{1+e} (any e>0). This answers a conjecture of Linnik for almost all natural numbers, and sharpens a conclusion of Bourgain, Rudnick and Sarnak concerning nearest neighbour distances between normalised integral points on the sphere.
Keywords
Cite
@article{arxiv.1302.1454,
title = {On Linnik's conjecture: sums of squares and microsquares},
author = {Trevor D. Wooley},
journal= {arXiv preprint arXiv:1302.1454},
year = {2022}
}