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Tr. Mat. Inst. Steklova, 2018, Volume 303, Pages 239–245 (Mi tm3944)  

Extremal properties of product sets

K. Ford

Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, USA

Abstract: We find the nearly optimal size of a set $A\subset [N] := \{1,…,N\}$ 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.


DOI: https://doi.org/10.1134/S0371968518040179

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 303, 220–226

Bibliographic databases:

UDC: 511.75
Received: January 27, 2018

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, Tr. 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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\pages 239--245
\publ MAIK Nauka/Interperiodica
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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