Some remarks on the Balog-Wooley decomposition theorem and quantities D^+, D^\times
Combinatorics
2016-05-03 v1 Number Theory
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.
Keywords
Cite
@article{arxiv.1605.00266,
title = {Some remarks on the Balog-Wooley decomposition theorem and quantities D^+, D^\times},
author = {Ilya D. Shkredov},
journal= {arXiv preprint arXiv:1605.00266},
year = {2016}
}
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20 pages