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arXiv · 1302.1454

On Linnik's conjecture: sums of squares and microsquares

Trevor D. Wooley
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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.

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Trevor D. Wooley. 2013-02-06. On Linnik's conjecture: sums of squares and microsquares. https://arxiv.org/abs/1302.1454

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