On Waring–Goldbach problem with Piatetski-Shapiro primes

Akbal Y., Güloğlu A. M.

Journal of Number Theory, vol.185, pp.80-92, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 185
  • Publication Date: 2018
  • Doi Number: 10.1016/j.jnt.2017.09.018
  • Journal Name: Journal of Number Theory
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.80-92
  • Keywords: Circle method, Exponential sums, Piatetski-Shapiro, van der Corput, Waring–Goldbach, Weyl sums
  • TED University Affiliated: No

Abstract

In this paper, we show that all sufficiently large natural numbers satisfying certain local conditions can be written as the sum of kth powers of Piatetski-Shapiro primes, thereby establishing a variant of Waring–Goldbach problem with primes from a sparse sequence.