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J. Number Theory, 2013, Volume 133, Issue 5, Pages 1693–1737 (Mi jnt4)  

Higher moments of convolutions

T. Schoena, I. D. Shkredovbcd

a Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
b Division of Algebra and Number Theory, Steklov Mathematical Institute, ul. Gubkina, 8, Moscow 119991, Russia
c IITP RAS, Bolshoy Karetny per. 19, Moscow 127994, Russia
d Delone Laboratory of Discrete and Computational Geometry, Yaroslavl State University, Sovetskaya str. 14, Yaroslavl 150000, Russia

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 06-01-00383
Ministry of Education and Science of the Russian Federation 11.G34.31.0053
2519.2012.1
Ministry of Science and Higher Education (Poland) N201 543538
The author is supported by MNSW grant N N201 543538. This work was supported by grant RFFI NN 06-01-00383, 11-01-00759, Russian Government project 11.G34.31.0053 and grant Leading Scientific Schools N 2519.2012.1.


DOI: https://doi.org/10.1016/j.jnt.2012.10.010


Bibliographic databases:

Document Type: Article
Received: 08.02.2012
Accepted:30.10.2012
Language: English

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