Distribution modulo 1 of some oscillating sequences. III

D. Berend, Michael D. Boshernitzan, Grigori Kolesnik

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

For some oscillating functions, such as h(x) = xπ log3 x cos x, we consider the distribution properties modulo 1 (density, uniform distribution) of the sequence h(n), n ≧ 1. We obtain positive and negative results covering the case when the factor xπ log3 x is replaced by an arbitrary function f of at most polynomial growth belonging to any Hardy field. (The latter condition may be viewed as a regularity growth condition on f.) Similar results are obtained for the subsequence h(p), taken over the primes p = 2, 3, 5,....

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalActa Mathematica Hungarica
Volume95
Issue number1-2
DOIs
StatePublished - 1 Apr 2002

Keywords

  • Density modulo 1
  • Distribution modulo 1
  • Exponential sums
  • Hardy field
  • Uniform distribution

ASJC Scopus subject areas

  • Mathematics (all)

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