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arXiv · 1410.1156

A bound on the multiplicative energy of a sum set and extremal sum-product problems

Oliver Roche-Newton·Dmitry Zhelezov
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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.

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Oliver Roche-Newton, Dmitry Zhelezov. 2014-10-05. A bound on the multiplicative energy of a sum set and extremal sum-product problems. https://arxiv.org/abs/1410.1156

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