Higher moments of convolutions |
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| Authors: | Tomasz Schoen Ilya D. Shkredov |
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| Affiliation: | 1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland;2. Division of Algebra and Number Theory, Steklov Mathematical Institute, ul. Gubkina, 8, Moscow 119991, Russia;3. Delone Laboratory of Discrete and Computational Geometry, Yaroslavl State University, Sovetskaya str. 14, Yaroslavl 150000, Russia;4. IITP RAS, Bolshoy Karetny per. 19, Moscow 127994, Russia |
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| 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. |
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