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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Volume 303, Pages 239–245
DOI: https://doi.org/10.1134/S0371968518040179 (Mi tm3944) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Extremal properties of product sets

K. Ford

Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, USA
Full-text PDF (186 kB) Citations (5)
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DOI: https://doi.org/10.1134/S0371968518040179
Abstract: We find the nearly optimal size of a set $A\subset [N] := \{1,\dots ,N\}$ so that the product set $AA$ satisfies either (i) $|AA| \sim |A|^2/2$ or (ii) $|AA| \sim |[N][N]|$. This settles problems recently posed in a paper of J. Cilleruelo, D. S. Ramana and O. Ramaré.
Funding agency Grant number
National Science Foundation DMS-1501982
DMS-1440140
The research of the author was supported in part by the individual NSF grant DMS-1501982. Some of this work was carried out at MSRI, Berkeley, during the Spring semester of 2017, partially supported by NSF grant DMS-1440140.
Received: January 27, 2018
English version:
Proceedings of the Steklov Institute of Mathematics, 2018, Volume 303, Pages 220–226
DOI: https://doi.org/10.1134/S0081543818080175
Bibliographic databases:
Document Type: Article
UDC: 511.75
Language: Russian
Citation: K. Ford, “Extremal properties of product sets”, Harmonic analysis, approximation theory, and number theory, Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday, Trudy Mat. Inst. Steklova, 303, MAIK Nauka/Interperiodica, Moscow, 2018, 239–245; Proc. Steklov Inst. Math., 303 (2018), 220–226
Citation in format AMSBIB
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\bookinfo Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2018
\vol 303
\pages 239--245
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • https://doi.org/10.1134/S0371968518040179
  • https://www.mathnet.ru/eng/tm/v303/p239
    • This publication is cited in the following 5 articles:
    1. Yu. N. Shteinikov, “Ob ekstremalnykh tselochislennykh mnozhestvakh v konechnykh intervalakh i ikh proizvedeniyakh”, Matem. zametki, 117:3 (2025), 453–461  mathnet  crossref
    2. Yu. N. Shteinikov, “Sets with Extremal Product Property and Its Variations”, Math. Notes, 114:6 (2023), 1342–1349  mathnet  crossref  crossref  mathscinet
    3. K. Soundararajan, M. W. Xu, “Central limit theorems for random multiplicative functions”, JAMA, 151:1 (2023), 343  crossref
    4. O. Ramaré, “The number of rationals determined by large sets of sifted integers”, Proc. Math. Sci., 132:2 (2022), 62  crossref
    5. D. Mastrostefano, “On maximal product sets of random sets”, J. Number Theory, 224 (2021), 13–40  crossref  mathscinet  isi
    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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