Vol. 8, No. 1, 2019

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Some remarks on the asymmetric sum-product phenomenon

Ilya D. Shkredov

Vol. 8 (2019), No. 1, 15–41
DOI: 10.2140/moscow.2019.8.15
Abstract

Using some new observations connected to higher energies, we obtain quantitative lower bounds on max{|AB|,|A + C|} and max{|AB|,|(A + α)C|}, where α0, in the regime when the sizes of the finite subsets A,B,C of a field differ significantly.

Keywords
sum-product, expanders, exponential sums
Mathematical Subject Classification 2010
Primary: 11B30, 11P70
Milestones
Received: 1 December 2017
Published: 11 August 2018
Authors
Ilya D. Shkredov
Steklov Mathematical Institute
ul. Gubkina, 9
Moscow
Russia
119991
IITP RAS
Bolshoy Karetny per. 19
Moscow
Russia
127994
MIPT
Institutskii per. 9
Dolgoprudnii
Russia
141701