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Izvestiya: Mathematics, 2014, Volume 78, Issue 4, Pages 656–707
DOI: https://doi.org/10.1070/IM2014v078n04ABEH002703 (Mi im8070) 		 
This article is cited in 40 scientific papers (total in 40 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 (40)
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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
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2014, Volume 78, Issue 4, Pages 19–72
DOI: https://doi.org/10.4213/im8070
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. RAN. Ser. Mat., 78:4 (2014), 19–72; Izv. Math., 78:4 (2014), 656–707
Citation in format AMSBIB
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  • https://doi.org/10.1070/IM2014v078n04ABEH002703
  • https://www.mathnet.ru/eng/im/v78/i4/p19
    • This publication is cited in the following 40 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:1566
    Russian version PDF:292
    English version PDF:10
    References:97
    First page:58
     
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