Some remarks on the Balog-Wooley decomposition theorem and quantities D^+, D^\times

Abstract

In the paper we study two characteristics D^+ (A), D^\times (A) of a set A which play important role in recent results concerning sum-product phenomenon. Also we obtain several variants and improvements of the Balog-Wooley decomposition theorem. In particular, we prove that any finite subset of real numbers can be split into two sets with small quantities D^+ and D^\times.

arXiv comment20 pages

Cited by in corpus (1)

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