On the Waring–Goldbach problem for eighth and higher powers

Angel V. Kumchev, Trevor D Wooley

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

5 Citations (Scopus)
325 Downloads (Pure)

Abstract

Recent progress on Vinogradov's mean value theorem has resulted in improved estimates for exponential sums of Weyl type. We apply these new estimates to obtain sharper bounds for the hunck H(k) in the Waring-Goldbach problem. We obtain new results for all exponents k8, and in particular establish that H(k) ≤ (4k - 2) log k + k - 7 when k is large, giving the first improvement on the classical result of Hua from the 1940s.
Original languageEnglish
Pages (from-to)811-824
Number of pages14
JournalJournal of the London Mathematical Society
Volume93
Issue number3
Early online date4 May 2016
DOIs
Publication statusPublished - Jun 2016

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