Open AccessMathematicsPhysics
Ilya D. Shkredov
tlooto Summary
New observations provide quantitative lower bounds on maximum absolute values of sums and products of finite subsets in a field under specific energetic conditions.
Abstract
Using some new observations connected to higher energies, we obtain quantitative lower bounds on $\max\{|AB|, |A+C| \}$ and $\max\{|(A+\alpha)B|, |A+C|\}$, $\alpha \neq 0$ in the regime when the sizes of finite subsets $A,B,C$ of a field differ significantly.
Citation format
SHKREDOV, Ilya D. Some remarks on the asymmetric sum--product phenomenon [preprint]. arXiv, 2017. arXiv:1705.09703.