A bound on the multiplicative energy of a sum set and extremal sum-product problems
Combinatorics
2014-10-07 v1 Number Theory
Abstract
In recent years some near-optimal estimates have been established for certain sum-product type estimates. This paper gives some first extremal results which provide information about when these bounds may or may not be tight. The main tool is a new result which provides a nontrivial upper bound on the multiplicative energy of a sum set or difference set.
Keywords
Cite
@article{arxiv.1410.1156,
title = {A bound on the multiplicative energy of a sum set and extremal sum-product problems},
author = {Oliver Roche-Newton and Dmitry Zhelezov},
journal= {arXiv preprint arXiv:1410.1156},
year = {2014}
}
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13 pages