On the exponential sum over k-free numbers

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

doi:10.1098/rsta.1998.0183

On the exponential sum over k-free numbers

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

Mathematics

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	739-761
Number of pages	23
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	356
Issue number	1738
DOIs	https://doi.org/10.1098/rsta.1998.0183
State	Published - Mar 15 1998

All Science Journal Classification (ASJC) codes

General Mathematics
General Engineering
General Physics and Astronomy

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10.1098/rsta.1998.0183

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On the exponential sum over k-free numbers

Abstract

All Science Journal Classification (ASJC) codes

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