Some new results on higher energies
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I. D. Shkredov
Translated by: Christopher Hollings - Trans. Moscow Math. Soc. 2013, 31-63
- DOI: https://doi.org/10.1090/S0077-1554-2014-00212-0
- Published electronically: April 9, 2014
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Abstract:
This article is concerned with the method of higher energies from combinatorial number theory. Upper bounds are obtained for the additive energies of convex sets and of sets $A$ with small $|AA|$ and $|A(A+1)|$. New structural results, involving the notion of a dual popular difference set, are proved in terms of higher energies.References
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Bibliographic Information
- I. D. Shkredov
- Affiliation: Department of Algebra and Number Theory, Russian Academy of Sciences, Steklov Mathematical Institute, Moscow; Delone Laboratory of Discrete and Computational Geometry, Yaroslavl State University, Yaroslavl; Kharkevich Institute of Information Transmission Problems, Russian Academy of Sciences
- MR Author ID: 705369
- Email: ilya.shkredov@gmail.com
- Published electronically: April 9, 2014
- Additional Notes: This work was supported by the grant RFFI 11-01-00759, the Government grant RF 11.G34.31.0053, the Federal Program “Scientific and Scientific-Pedagogical Personnel in Russia” 2009–2013, the Grant for Scientific Projects Undertaken by Leading Youth Collectives 12-01-33080, and the Grant for Leading Scientific Schools 2519.2012.1.
- © Copyright 2014 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2013, 31-63
- MSC (2010): Primary 11B30; Secondary 11B75
- DOI: https://doi.org/10.1090/S0077-1554-2014-00212-0
- MathSciNet review: 3235789