ON THE EXPONENTIAL SUM OVER K-FREE NUMBERS

Authors
BRUDERN J GRANVILLE A PERELLI A VAUGHAN RC WOOLEY TD
Citation
J. Brudern et al., ON THE EXPONENTIAL SUM OVER K-FREE NUMBERS, Philosophical transactions-Royal Society of London. Physical sciences and engineering, 356(1738), 1998, pp. 739-761
Citations number
15
Categorie Soggetti
Multidisciplinary Sciences
Journal title
Philosophical transactions-Royal Society of London. Physical sciences and engineering → ACNP
ISSN journal
09628428
Volume
356
Issue
1738
Year of publication
1998
Pages
739 - 761
Database
ISI
SICI code
0962-8428(1998)356:1738<739:OTESOK>2.0.ZU;2-P
Abstract
This paper is concerned with mean values of exponential sum generating functions over k-free numbers, and especially their L-1-means. We als o provide non-trivial estimates for the L-2-means of such generating f unctions restricted to the minor arcs occurring in Hardy-Littlewood di ssections, thereby permitting the circle method to be successfully app lied to certain additive problems hitherto beyond its reach.