On the Waring–Goldbach problem for seventh and higher powers

Angel Kumchev, Trevor D Wooley

Research output: Contribution to journalArticle (Academic Journal)peer-review

10 Citations (Scopus)
133 Downloads (Pure)

Abstract

We apply recent progress on Vinogradov's mean value theorem to improve bounds for the function H(k) in the Waring-Goldbach problem. We obtain new results for all exponents k7, and in particular establish that for large k one has H(k)(4k2)logk−(2log2−1)k−3.
Original languageEnglish
Pages (from-to)303–310
Number of pages8
JournalMonatshefte für Mathematik
Volume183
Issue number2
Early online date15 Jun 2016
DOIs
Publication statusPublished - 5 May 2017

Keywords

  • Vinogradov mean-value theorem
  • Waring–Goldbach problem
  • Weyl sums

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