On the exponential sum over k-free numbers

J. Brüdern, A. Granville, A. Perelli, R. C. Vaughan, T. D. Wooley

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


This paper is concerned with mean values of exponential sum generating functions over k-free numbers, and especially their L1-means. We also provide non-trivial estimates for the L2-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 (US)
Pages (from-to)739-761
Number of pages23
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1738
StatePublished - Mar 15 1998

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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