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arXiv · 1705.09703

Some remarks on the asymmetric sum--product phenomenon

Ilya D. Shkredov
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Abstract

Using some new observations connected to higher energies, we obtain quantitative lower bounds on $\max\{|AB|, |A+C| \}$ and $\max\{|(A+α)B|, |A+C|\}$, $α\neq 0$ in the regime when the sizes of finite subsets $A,B,C$ of a field differ significantly.

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Ilya D. Shkredov. 2017-05-26. Some remarks on the asymmetric sum--product phenomenon. https://doi.org/10.2140/moscow.2019.8.15

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