Rough values of Piatetski-Shapiro sequences

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Akbal Y.

Monatshefte fur Mathematik, vol.185, no.1, pp.1-15, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 185 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.1007/s00605-016-0993-y
  • Journal Name: Monatshefte fur Mathematik
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1-15
  • Keywords: Exponential sums, Piatetski-Shapiro sequences, Rough numbers
  • TED University Affiliated: No

Abstract

An integer is called y-rough if it is composed solely of primes CloseSPigtSPi y. Let ⌊. ⌋ be the floor function. In this paper, we exhibit an asymptotic formula for the counting function of integers n⩽ x such that ⌊ nc⌋ is y-rough uniformly for a range of y that depends on 1 OpenSPiltSPi cOpenSPiltSPi 2229 / 1949.