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Tr. Mosk. Mat. Obs., 2013, Volume 74, Issue 1, Pages 35–73 (Mi mmo540)  

This article is cited in 9 scientific papers (total in 9 papers)

Some new results on higher energies

I. D. Shkredovab

a Steklov Mathematical Institute of the Russian Academy of Sciences
b Delone Laboratory of Discrete and Computational Geometry, P. G. Demidov Yaroslavl State University

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.

Key words and phrases: combinatorial number theory; higher energies; popular difference set.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0053
2519.2012.1
Russian Foundation for Basic Research 11-01-00759_а
12-01-33080_мол_а_вед


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English version:
Transactions of the Moscow Mathematical Society, 2013, 74, 31–63

Bibliographic databases:

Document Type: Article
UDC: 511.37
MSC: 11H99
Received: 30.12.2012
Revised: 17.02.2013

Citation: I. D. Shkredov, “Some new results on higher energies”, Tr. Mosk. Mat. Obs., 74, no. 1, MCCME, M., 2013, 35–73; Trans. Moscow Math. Soc., 74 (2013), 31–63

Citation in format AMSBIB
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\by I.~D.~Shkredov
\paper Some new results on higher energies
\serial Tr. Mosk. Mat. Obs.
\yr 2013
\vol 74
\issue 1
\pages 35--73
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo540}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3235789}
\zmath{https://zbmath.org/?q=an:06371555}
\elib{http://elibrary.ru/item.asp?id=21369363}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2013
\vol 74
\pages 31--63
\crossref{https://doi.org/10.1090/S0077-1554-2014-00212-0}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84929260312}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Shkredov I.D., “on Exponential Sums Over Multiplicative Subgroups of Medium Size”, Finite Fields their Appl., 30 (2014), 72–87  crossref  mathscinet  zmath  isi  elib  scopus
    2. Ilya Sh., “Energies and Structure of Additive Sets”, Electron. J. Comb., 21:3 (2014), P3.44  zmath  isi
    3. I. D. Shkredov, “Structure theorems in additive combinatorics”, Russian Math. Surveys, 70:1 (2015), 113–163  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. I. D. Shkredov, “On sums of Szemerédi–Trotter sets”, Proc. Steklov Inst. Math., 289 (2015), 300–309  mathnet  crossref  crossref  isi  elib
    5. I. D. Shkredov, “On a question of A. Balog”, Pac. J. Math., 280:1 (2016), 227–240  crossref  mathscinet  zmath  isi  elib  scopus
    6. T. Schoen, I. D. Shkredov, “Additive dimension and a theorem of Sanders”, J. Aust. Math. Soc., 100:1 (2016), 124–144  crossref  mathscinet  zmath  isi  scopus
    7. I. V. Vyugin, E. V. Solodkova, I. D. Shkredov, “On the Additive Energy of the Heilbronn Subgroup”, Math. Notes, 101:1 (2017), 58–70  mathnet  crossref  crossref  mathscinet  isi  elib
    8. B. Murphy, O. Roche-Newton, I. D. Shkredov, “Variations on the Sum-Product Problems II”, SIAM Discret. Math., 31:3 (2017), 1878–1894  crossref  mathscinet  zmath  isi  scopus
    9. I. D. Shkredov, “On asymptotic formulae in some sum-product questions”, Trans. Moscow Math. Soc., 2018, 231–281  mathnet  crossref  elib
  • Trudy Moskovskogo Matematicheskogo Obshchestva
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