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Monatshefte für Mathematik

, Volume 185, Issue 1, pp 1–15 | Cite as

Rough values of Piatetski-Shapiro sequences

  • Yıldırım Akbal
Article
  • 101 Downloads

Abstract

An integer is called y-rough if it is composed solely of primes \(> y\). Let \(\lfloor {.}\rfloor \) be the floor function. In this paper, we exhibit an asymptotic formula for the counting function of integers \(n \leqslant x\) such that \(\lfloor {n^c}\rfloor \) is y-rough uniformly for a range of y that depends on \(1< c < 2229/1949\).

Keywords

Piatetski-Shapiro sequences Rough numbers Exponential sums 

Mathematics Subject Classification

Primary 11N25 Secondary 11L07 

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Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  1. 1.Department of MathematicsBilkent UniversityAnkaraTurkey

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