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)|
|Number of pages||23|
|Journal||Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|State||Published - Mar 15 1998|
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)