Vinogradov's mean value theorem via efficient congruencing

Trevor D. Wooley*

*Corresponding author for this work

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

68 Citations (Scopus)
394 Downloads (Pure)

Abstract

We obtain estimates for Vinogradov's integral that for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided. In particular, the conjectured asymptotic formula in Waring's problem holds for sums of 8 kth powers of natural numbers whenever s >= 2k2 + 2k - 3.

Translated title of the contributionVinogradov's mean value theorem via efficient congruencing
Original languageEnglish
Pages (from-to)1575-1627
Number of pages53
JournalAnnals of Mathematics
Volume175
Issue number3
DOIs
Publication statusPublished - May 2012

Keywords

  • Waring's problem
  • Exponential sums
  • Hardy-Littlewood method

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