Let $calS$ denote the set of integers representable as a sum of twosquares. Since $calS$ can be described as the unsifted elements of asieving process of positive dimension, it is to be expected that$calS$ has many properties in common with the set of prime numbers.In this paper we exhibit ``unexpected irregularities'' in thedistribution of sums of two squares in short intervals, a phenomenonanalogous to that discovered by Maier, over a decade ago, in thedistribution of prime numbers. To be precise, we show that there areinfinitely many short intervals containing considerably more elementsof $calS$ than expected, and infinitely many intervals containingconsiderably fewer than expected.
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