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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A sum-division estimate of reals


Authors: Liangpan Li and Jian Shen
Journal: Proc. Amer. Math. Soc. 138 (2010), 101-104
MSC (2000): Primary 11B75
Published electronically: August 24, 2009
MathSciNet review: 2550173
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Abstract: Let $ A$ be a finite set of positive real numbers. We present a sum-division estimate:

$\displaystyle \vert A+A\vert^2\vert A/A\vert\geq\frac{\vert A\vert^4}{4}.$


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Additional Information

Liangpan Li
Affiliation: Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China – and – Department of Mathematics, Texas State University, San Marcos, Texas 78666
Email: liliangpan@yahoo.com.cn

Jian Shen
Affiliation: Department of Mathematics, Texas State University, San Marcos, Texas 78666
Email: js48@txstate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10052-7
PII: S 0002-9939(09)10052-7
Keywords: Sum-product estimate, sum-division estimate
Received by editor(s): May 12, 2009
Received by editor(s) in revised form: May 18, 2009
Published electronically: August 24, 2009
Communicated by: Ken Ono
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.