Sums of two squares in short intervals

James Maynard

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arXiv · 1910.13384

Sums of two squares in short intervals

James Maynard

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Abstract

We show that there are short intervals $[x,x+y]$ containing $\gg y^{1/10}$ numbers expressible as the sum of two squares, which is many more than the average when $y=o( (\log{x})^{5/9})$. We obtain similar results for sums of two squares in short arithmetic progressions.

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James Maynard. 2019-10-29. Sums of two squares in short intervals. https://arxiv.org/abs/1910.13384

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