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Sums of two squares in short intervals
Published 29 Oct 2019 in math.NT | (1910.13384v1)
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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