Exceptional Sets for Diophantine Inequalities

Scott T. Parsell*, Trevor D. Wooley

*Corresponding author for this work

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

4 Citations (Scopus)

Abstract

We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument. Under appropriate conditions, we show that the exceptional set in the interval [-N,N] has measure O(N1-delta), for a positive number delta.

Original languageEnglish
Pages (from-to)3919-3974
Number of pages56
JournalInternational Mathematics Research Notices
Issue number14
DOIs
Publication statusPublished - 2014

Keywords

  • MEAN-VALUE THEOREM
  • LATTICE POINT PROBLEMS
  • SMOOTH WEYL SUMS
  • WARINGS PROBLEM
  • ADDITIVE REPRESENTATION
  • ASYMPTOTIC FORMULAS
  • SMALLER EXPONENTS
  • QUADRATIC-FORMS
  • THIN SEQUENCES
  • HIGHER POWERS

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