## Abstract

Let S denote the set of integers representable as a sum of two squares. Since S can be described as the unsifted elements of a sieving process of positive dimension, it is to be expected that S has many properties in common with the set of prime numbers. In this paper we exhibit "unexpected irregularities" in the distribution of sums of two squares in short intervals, a phenomenon analogous to that discovered by Maier, over a decade ago, in the distribution of prime numbers. To be precise, we show that there are infinitely many short intervals containing considerably more elements of S than expected, and infinitely many intervals containing considerably fewer than expected.

Original language | English |
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Pages (from-to) | 673-694 |

Number of pages | 22 |

Journal | Canadian Journal of Mathematics . Journal Canadien de Mathematiques |

Volume | 52 |

Issue number | 4 |

Publication status | Published - Aug 2000 |

## Keywords

- sums of two squares
- sieves
- short intervals
- smooth numbers
- 2 SQUARES
- NUMBERS