Sums of two squares in short intervals - Maynard, J (Springer International Publishing, 2015)
Analytic Number Theory: In Honor of Helmut Maier’s 60th Birthday. We show that there are short intervals [x, x + y] containing ≫ y 1∕10 numbers expressible as the sum of two squares, which is many more than the average when y=o((logx)5/9)y=o((log⁡x)5/9). We obtain similar results for sums of two squares in short arithmetic progressions.