Higher moments of convolutions

2011/10/13 by Tomasz Schoen, Schoen, Tomasz, Ilya D. Shkredov +1 · 3 citations
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1110.2986

46 pages

arxiv created 2012/09/21 · arxiv updated 2012/09/24

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.

Cited by

• More on the sum-product problem for integers with few prime factors
• Optimal Young's convolutions inequality and its reverse form on the hypercube
• Inequalities in Fourier analysis on binary cubes

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