Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415629 | Journal of Number Theory | 2013 | 45 Pages |
Abstract
We study higher moments of convolutions of the characteristic function of a set, which generalize a classical notion of the additive energy. Such quantities appear in many problems of additive combinatorics as well as in number theory. In our investigation we use different approaches including basic combinatorics, Fourier analysis and eigenvalues method to establish basic properties of higher energies. We provide also a sequence of applications of higher energies additive combinatorics.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Tomasz Schoen, Ilya D. Shkredov,