Sums of two squares in short intervals

A Balog*, TD Wooley

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

6 Citations (Scopus)

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 languageEnglish
Pages (from-to)673-694
Number of pages22
JournalCanadian Journal of Mathematics . Journal Canadien de Mathematiques
Volume52
Issue number4
Publication statusPublished - Aug 2000

Keywords

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

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