Sums of two squares in short intervals

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.

18 pages; old article in Springer Volume dedicated to Helmut Maier