Near-Optimal Mean Value Estimates for Multidimensional Weyl Sums

Scott T. Parsell*, Sean M. Prendiville, Trevor D. Wooley

*Corresponding author for this work

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

20 Citations (Scopus)

Abstract

We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed.

Original languageEnglish
Pages (from-to)1962-2024
Number of pages63
JournalGeometric and Functional Analysis
Volume23
Issue number6
Early online date6 Jul 2013
DOIs
Publication statusPublished - Dec 2013

Keywords

  • VALUE THEOREM
  • POINTS

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