Pair correlation of fractional parts derived from rational valued sequences, II

Sneha Chaubey, Melinda Lanius, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

A rational valued vector sequence x→, for some fixed k and r∈N, is a map x→:Nk→Qr. In the present paper, we complement the results of [3] with a discussion on rational valued vector sequences. We investigate the pair correlation function for the fractional parts of sequences t→{dot operator}x→, where x→ is a rational valued vector sequence and t→∈Rr. We offer a new class of sequences x→ whose pair correlation function behaves as that of random sequences for almost all real vectors t→, namely, injective sequences of the formx→(m,n)=(p1mp2nb→(m,n),p3mp4nb→(m,n)) for p1, p2, p3, and p4 primes and where b→:N2→N satisfies a certain growth condition.

Original languageEnglish (US)
Pages (from-to)151-164
Number of pages14
JournalJournal of Number Theory
Volume158
DOIs
StatePublished - Jan 1 2016

Keywords

  • Fractional parts
  • Pair correlation
  • Rational valued sequences
  • Vector sequences

ASJC Scopus subject areas

  • Algebra and Number Theory

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