Loading [MathJax]/jax/output/CommonHTML/jax.js
Trudy Moskovskogo Matematicheskogo Obshchestva
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Journal history

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Tr. Mosk. Mat. Obs.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Trudy Moskovskogo Matematicheskogo Obshchestva, 2013, Volume 74, Issue 1, Pages 35–73 (Mi mmo540)  
This article is cited in 27 scientific papers (total in 27 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
Full-text PDF (428 kB) Citations (27)
References:
PDF
HTML
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
Received: 30.12.2012
Revised: 17.02.2013
English version:
Transactions of the Moscow Mathematical Society, 2013, Volume 74, Pages 31–63
DOI: https://doi.org/10.1090/S0077-1554-2014-00212-0
Bibliographic databases:
Document Type: Article
UDC: 511.37
MSC: 11H99
Language: Russian
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
\Bibitem{Shk13}
\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://mathscinet.ams.org/mathscinet-getitem?mr=3235789}
\zmath{https://zbmath.org/?q=an:06371555}
\elib{https://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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84929260312}
Linking options:
  • https://www.mathnet.ru/eng/mmo540
  • https://www.mathnet.ru/eng/mmo/v74/i1/p35
    • This publication is cited in the following 27 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Trudy Moskovskogo Matematicheskogo Obshchestva
    Statistics & downloads:
    Abstract page:638
    Full-text PDF :138
    References:61
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025