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) |
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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 | |
State | Published - Mar 15 1998 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)