Rough values of Piatetski-Shapiro sequences
Monatshefte fur Mathematik, vol.185, no.1, pp.1-15, 2018 (SCI-Expanded, Scopus)
- 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
- Open Archive Collection: AVESIS Open Access Collection
- 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.