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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Volume 296, Pages 58–71
DOI: https://doi.org/10.1134/S0371968517010058 (Mi tm3791) 		 
This article is cited in 19 scientific papers (total in 19 papers)

Quotient and product sets of thin subsets of the positive integers

J. Cillerueloab, D. S. Ramanac, O. Ramaréd

a Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), 28049 Madrid, Spain
b Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
c Harish-Chandra Research Institute, Jhunsi, Allahabad 211 019, India
d CNRS/ Institut de Mathématiques de Marseille, Aix Marseille Université, UMR 7373, Site Sud, Campus de Luminy, Case 907, 13288 Marseille Cedex 9, France
Full-text PDF (230 kB) Citations (19)
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DOI: https://doi.org/10.1134/S0371968517010058
Abstract: We study the cardinalities of $A/A$ and $AA$ for thin subsets $A$ of the set of the first $n$ positive integers. In particular, we consider the typical size of these quantities for random sets $A$ of zero density and compare them with the sizes of $A/A$ and $AA$ for subsets of the shifted primes and the set of sums of two integral squares.
Funding agency Grant number
Centre National de la Recherche Scientifique
The second author thanks the Indo-French Program in Mathematics of the CNRS, France, whose support made this collaboration possible.
Received: May 25, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2017, Volume 296, Pages 52–64
DOI: https://doi.org/10.1134/S0081543817010059
Bibliographic databases:
Document Type: Article
UDC: 511.75
Language: Russian
Citation: J. Cilleruelo, D. S. Ramana, O. Ramaré, “Quotient and product sets of thin subsets of the positive integers”, Analytic and combinatorial number theory, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 296, MAIK Nauka/Interperiodica, Moscow, 2017, 58–71; Proc. Steklov Inst. Math., 296 (2017), 52–64
Citation in format AMSBIB
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\paper Quotient and product sets of thin subsets of the positive integers
\inbook Analytic and combinatorial number theory
\bookinfo Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov
\serial Trudy Mat. Inst. Steklova
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\vol 296
\pages 58--71
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    Addendum
    This publication is cited in the following 19 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
     
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