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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

Online
ISSN
1435-5337
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Volume 27, Issue 3

Issues

Product graphs, sum-product graphs and sum-product estimates over finite rings

Le Anh Vinh
Published Online: 2013-04-30 | DOI: https://doi.org/10.1515/forum-2012-0177

Abstract

In this paper, we study the product and sum-product graphs defined over the residue ring mod m. We show that all (or almost all) systems of dot-product equations are solvable in any sufficiently large subset ℰ ⊂ ℤmd. We also prove some results on sum-product estimates in ℤm.

Keywords: Bilinear equations; product graphs; sum-product graphs; sum-product estimates

MSC: 15A15

About the article

Received: 2012-12-12

Revised: 2013-02-25

Published Online: 2013-04-30

Published in Print: 2015-05-01


Funding Source: Vietnam National Foundation for Science and Technology Development

Award identifier / Grant number: 101.01-2011.28


Citation Information: Forum Mathematicum, Volume 27, Issue 3, Pages 1639–1655, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0177.

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[1]
Le Quang Ham, Pham Van Thang, and Le Anh Vinh
European Journal of Combinatorics, 2017, Volume 60, Page 114

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