Pair correlation of sums of rationals with bounded height

Emre Alkan, Maosheng Xiong, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

For each positive integer Q, let ℱQ denote the Farey sequence of order Q. We prove the existence of the pair correlation measure associated to the sum ℱQ + ℱQ modulo 1, as Q tends to infinity, and compute the corresponding limiting pair correlation function.

Original languageEnglish (US)
Pages (from-to)21-67
Number of pages47
JournalJournal fur die Reine und Angewandte Mathematik
Issue number641
DOIs
StatePublished - Apr 2010

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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