RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2018, Volume 103, Issue 2, Pages 273–294 (Mi mz11319)  

On Two-Dimensional Sums in Abelian Groups

A. A. Uvakin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: It is proved that if, for a subset $A$ of a finite Abelian group $G$, under the action of a linear operator $L\colon G^3 \to G^2$, the image $L(A,A,A)$ has cardinality less than $(7/4)|A|^2$, then there exists a subgroup $H \subseteq G$ and an element $x \in G$ for which $A \subseteq H+x$; further, $|H| < (3/2)|A|$.

Keywords: Abelian group, linear operator, convolution, sums of sets, additive combinatorics.

Funding Agency Grant Number
Russian Science Foundation 14-11-00433
This work was supported by the Russian Science Foundation under grant 14-11-00433.


DOI: https://doi.org/10.4213/mzm11319

Full text: PDF file (529 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Mathematical Notes, 2018, 103:2, 271–289

Bibliographic databases:

UDC: 512.541
Received: 21.07.2016
Revised: 01.03.2017

Citation: A. A. Uvakin, “On Two-Dimensional Sums in Abelian Groups”, Mat. Zametki, 103:2 (2018), 273–294; Math. Notes, 103:2 (2018), 271–289

Citation in format AMSBIB
\Bibitem{Uva18}
\by A.~A.~Uvakin
\paper On Two-Dimensional Sums in Abelian Groups
\jour Mat. Zametki
\yr 2018
\vol 103
\issue 2
\pages 273--294
\mathnet{http://mi.mathnet.ru/mz11319}
\crossref{https://doi.org/10.4213/mzm11319}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3749611}
\elib{http://elibrary.ru/item.asp?id=32428094}
\transl
\jour Math. Notes
\yr 2018
\vol 103
\issue 2
\pages 271--289
\crossref{https://doi.org/10.1134/S0001434618010285}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000427616800028}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85043768724}


Linking options:
  • http://mi.mathnet.ru/eng/mz11319
  • https://doi.org/10.4213/mzm11319
  • http://mi.mathnet.ru/eng/mz/v103/i2/p273

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математические заметки Mathematical Notes
    Number of views:
    This page:190
    References:21
    First page:11

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020