Vol. 8, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
ISSN (electronic): 2640-7361
ISSN (print): 2220-5438
Previously Published
To Appear
founded and published with the
scientific support and advice of the
Moscow Institute of
Physics and Technology
 
Other MSP Journals
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