On the exponential sum over k-free numbers

J Brudern*, A Granville, A Perelli, RC Vaughan, TD Wooley

*Corresponding author for this work

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

16 Citations (Scopus)

Abstract

This paper is concerned with mean values of exponential sum generating functions over k-free numbers, and especially their L-1-means. We also provide non-trivial estimates for the L-2-means of such generating functions restricted to the minor arcs occurring in Hardy-Littlewood dissections, thereby permitting the circle method to be successfully applied to certain additive problems hitherto beyond its reach.

Original languageEnglish
Pages (from-to)739-761
Number of pages23
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume356
Issue number1738
Publication statusPublished - 15 Mar 1998

Keywords

  • L-1-means
  • k-free numbers
  • exponential sums
  • Hardy-Littlewood method
  • binary additive representations
  • square-free numbers
  • WARINGS PROBLEM

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