A short note on some arithmetical properties of the integer part of αp

Akbal Y.

Turkish Journal of Mathematics, vol.43, no.3, pp.1253-1262, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.3906/mat-1809-43
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1253-1262
  • Keywords: Arithmetic progressions, Beatty sequences, Exponential sums, Shifted primes
  • TED University Affiliated: No

Abstract

Let α > 0 be an irrational number. We study some of the arithmetical properties of [⌊αp⌋]p=2∞, where p denotes a prime number and ⌊x⌋ denotes the largest integer not exceeding x.