Higher moments of convolutions

Details Higher moments of convolutions Higher moments of convolutions

2011-10-13

arxiv.org/abs/1110.2986v2

Mathematics

Combinatorics

36 pages

Scientific paper

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.

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