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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find




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

Izvestiya: Mathematics, 2014, Volume 78, Issue 4, Pages 656–707
DOI: https://doi.org/10.1070/IM2014v078n04ABEH002703 (Mi im8070) 		 
This article is cited in 37 scientific papers (total in 37 papers)

Sumsets of reciprocals in prime fields and multilinear Kloosterman sums

J. Bourgaina, M. Z. Garaevb

a Institute for Advanced Study, School of Mathematics
b National Autonomous University of Mexico, Institute of Mathematics
English version PDF (537 kB) Citations (37) Russian version article
References:
PDF
HTML
DOI: https://doi.org/10.1070/IM2014v078n04ABEH002703
Abstract: We obtain new results on the additive properties of the set $I^{-1}=\{x^{-1}\colon x\in I\}$, where $I$ is an arbitrary interval in the field of residue classes modulo a large prime $p$. Combining our results with estimates of multilinear exponential sums, we obtain new results on incomplete multilinear Kloosterman sums.
Keywords: congruences modulo a prime, sumsets, multilinear exponential sums, multilinear Kloosterman sums, distribution of primes.
Received: 20.11.2012
Revised: 22.07.2013
Bibliographic databases:
Document Type: Article
MSC: 11L05, 11L07, 11N05
Language: English
Original paper language: Russian
Citation: J. Bourgain, M. Z. Garaev, “Sumsets of reciprocals in prime fields and multilinear Kloosterman sums”, Izv. Math., 78:4 (2014), 656–707
Citation in format AMSBIB
\Bibitem{BouGar14}
\by J.~Bourgain, M.~Z.~Garaev
\paper Sumsets of reciprocals in prime fields and multilinear Kloosterman sums
\jour Izv. Math.
\yr 2014
\vol 78
\issue 4
\pages 656--707
\mathnet{http://mi.mathnet.ru//eng/im8070}
\crossref{https://doi.org/10.1070/IM2014v078n04ABEH002703}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3288401}
\zmath{https://zbmath.org/?q=an:06358162}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2014IzMat..78..656B}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000344454600002}
\elib{https://elibrary.ru/item.asp?id=21826427}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84907350952}
Linking options:
  • https://www.mathnet.ru/eng/im8070
  • https://doi.org/10.1070/IM2014v078n04ABEH002703
  • https://www.mathnet.ru/eng/im/v78/i4/p19
    • This publication is cited in the following 37 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:1617
    Russian version PDF:312
    English version PDF:15
    References:107
    First page:58
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024