Involve: A Journal of Mathematics
- Volume 2, Number 5 (2009), 603-609.
Some results on the size of sum and product sets of finite sets of real numbers
Let and be finite subsets of positive real numbers. Solymosi gave the sum-product estimate , where is the ceiling function. We use a variant of his argument to give the bound
(This isn’t quite a generalization since the logarithmic losses are worse here than in Solymosi’s bound.)
Suppose that is a finite subset of real numbers. We show that there exists an such that for some absolute constant .
Involve, Volume 2, Number 5 (2009), 603-609.
Received: 7 September 2009
Accepted: 12 November 2009
First available in Project Euclid: 20 December 2017
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Hart, Derrick; Niziolek, Alexander. Some results on the size of sum and product sets of finite sets of real numbers. Involve 2 (2009), no. 5, 603--609. doi:10.2140/involve.2009.2.603. https://projecteuclid.org/euclid.involve/1513799214