Trudy Matematicheskogo Instituta imeni V.A. Steklova
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
Find




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

Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Volume 280, Pages 67–96
DOI: https://doi.org/10.1134/S0371968513010056 (Mi tm3445) 		 
This article is cited in 32 scientific papers (total in 32 papers)

On congruences with products of variables from short intervals and applications

Jean Bourgaina, Moubariz Z. Garaevb, Sergei V. Konyaginc, Igor E. Shparlinskid

a Institute for Advanced Study, Princeton, NJ, USA
b Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Morelia, Michoacán, México
c Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
d Department of Computing, Macquarie University, Sydney, NSW, Australia
Full-text PDF (327 kB) Citations (32)
References:
PDF
HTML
DOI: https://doi.org/10.1134/S0371968513010056
Abstract: We obtain upper bounds on the number of solutions to congruences of the type $(x_1+s)\dots(x_\nu+s)\equiv(y_1+s)\dots(y_\nu +s)\not\equiv0\pmod p$ modulo a prime $p$ with variables from some short intervals. We give some applications of our results and in particular improve several recent estimates of J. Cilleruelo and M. Z. Garaev on exponential congruences and on cardinalities of products of short intervals, some double character sum estimates of J. Friedlander and H. Iwaniec and some results of M.-C. Chang and A. A. Karatsuba on character sums twisted with the divisor function.
Funding agency Grant number
National Science Foundation DMS-0808042
Russian Foundation for Basic Research 11-01-00329
Ministry of Education and Science of the Russian Federation NSh-6003.2012.1
Australian Research Council DP1092835
The research was partially supported by National Science Foundation grant DMS-0808042 (J.B.), by the Russian Foundation for Basic Research (project no. 11-01-00329, S.V.K.), by a grant of the President of the Russian Federation (project no. NSh-6003.2012.1, S.V.K.), and by Australian Research Council grant DP1092835 (I.E.S.).
Received in January 2012
English version:
Proceedings of the Steklov Institute of Mathematics, 2013, Volume 280, Pages 61–90
DOI: https://doi.org/10.1134/S0081543813010057
Bibliographic databases:
Document Type: Article
UDC: 511.3+511.524
Language: English
Citation: Jean Bourgain, Moubariz Z. Garaev, Sergei V. Konyagin, Igor E. Shparlinski, “On congruences with products of variables from short intervals and applications”, Orthogonal series, approximation theory, and related problems, Collected papers. Dedicated to Academician Boris Sergeevich Kashin on the occasion of his 60th birthday, Trudy Mat. Inst. Steklova, 280, MAIK Nauka/Interperiodica, Moscow, 2013, 67–96; Proc. Steklov Inst. Math., 280 (2013), 61–90
Citation in format AMSBIB
\Bibitem{BouGarKon13}
\by Jean~Bourgain, Moubariz~Z.~Garaev, Sergei~V.~Konyagin, Igor~E.~Shparlinski
\paper On congruences with products of variables from short intervals and applications
\inbook Orthogonal series, approximation theory, and related problems
\bookinfo Collected papers. Dedicated to Academician Boris Sergeevich Kashin on the occasion of his 60th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2013
\vol 280
\pages 67--96
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3445}
\crossref{https://doi.org/10.1134/S0371968513010056}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3241837}
\elib{https://elibrary.ru/item.asp?id=18893030}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2013
\vol 280
\pages 61--90
\crossref{https://doi.org/10.1134/S0081543813010057}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000320459700005}
\elib{https://elibrary.ru/item.asp?id=21878021}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84871571740}
Linking options:
  • https://www.mathnet.ru/eng/tm3445
  • https://doi.org/10.1134/S0371968513010056
  • https://www.mathnet.ru/eng/tm/v280/p67
    • This publication is cited in the following 32 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Statistics & downloads:
    Abstract page:880
    Full-text PDF :84
    References:86
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024