Waring–Goldbach problem with Piatetski-Shapiro primes

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Akbal Y., Güloğlu A. M.

Journal de Theorie des Nombres de Bordeaux, vol.30, no.2, pp.449-467, 2018 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 30 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.5802/jtnb.1033
  • Journal Name: Journal de Theorie des Nombres de Bordeaux
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.449-467
  • Keywords: Circle method, Exponential sums, Piatetski-Shapiro primes, van der Corput’s method, Vinogradov’s mean value theorem, Waring-Goldbach problem, Weyl sums
  • Open Archive Collection: AVESIS Open Access Collection
  • TED University Affiliated: No

Abstract

In this paper, we exhibit an asymptotic formula for the number of representations of a large integer as a sum of a fixed power of Piatetski-Shapiro primes, thereby establishing a variant of Waring–Goldbach problem with primes from a sparse sequence.