RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Guidelines for authors License agreement Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Trudy MIAN: Year: Volume: Issue: Page: Find

 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-1501982DMS-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

Full text: PDF file (186 kB)
First page: PDF file
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 511.75

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
\Bibitem{For18} \by K.~Ford \paper Extremal properties of product sets \inbook Harmonic analysis, approximation theory, and number theory \bookinfo Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday \serial Tr. Mat. Inst. Steklova \yr 2018 \vol 303 \pages 239--245 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3944} \crossref{https://doi.org/10.1134/S0371968518040179} \elib{http://elibrary.ru/item.asp?id=37045264} \transl \jour Proc. Steklov Inst. Math. \yr 2018 \vol 303 \pages 220--226 \crossref{https://doi.org/10.1134/S0081543818080175} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000460475900017} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85062501079}