Relations between exceptional sets for additive problems

Koichi Kawada*, Trevor D. Wooley

*Corresponding author for this work

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

9 Citations (Scopus)

Abstract

We describe a method for bounding the set of exceptional integers not represented by a given additive form in terms of the exceptional set corresponding to a subform. Illustrating our ideas with examples stemming from Waring's problem for cubes, we show, in particular, that the number of positive integers not exceeding N that fail to have a representation as the sum of six cubes of natural numbers is O(N(3/7)).

Original languageEnglish
Pages (from-to)437-458
Number of pages22
JournalJournal of the London Mathematical Society
Volume82
DOIs
Publication statusPublished - Oct 2010

Keywords

  • WARINGS PROBLEM
  • HIGHER POWERS
  • SUMS
  • CUBES
  • IMPROVEMENTS
  • SQUARES
  • NUMBER

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