Additive representation in thin sequences, VI: Representing primes, and related problems

J Brudern, K Kawada, TD Wooley

Research output: Contribution to journalArticle (Academic Journal)

Abstract

We discuss the representation of primes, almost-primes, and related arithmetic sequences as sums of kth powers of natural numbers. In particular, we show that on GRH, there are infinitely many primes represented as the sum of 2[4k/3] positive integral kth powers, and we prove unconditionally that infinitely many P-2-numbers are the sum of 2k + I positive integral kth powers. The sieve methods required to establish the latter conclusion demand that we investigate the distribution of sums of kth powers in arithmetic progressions, and our conclusions here may be of independent interest.
Translated title of the contributionAdditive representation in thin sequences, VI: Representing primes, and related problems
Original languageEnglish
Pages (from-to)419 - 434
Number of pages26
JournalGlasgow Mathematical Journal
Volume44 (3
DOIs
Publication statusPublished - Sep 2002

Bibliographical note

Publisher: Cambridge Univ Press

Keywords

  • WARINGS PROBLEM
  • CUBES
  • IMPROVEMENTS
  • POWER
  • IV

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