Vol. 8, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Volume 8, Issue 1
The Journal
About the Journal
Subscriptions
Editorial Board
Submission Guidelines
Submission Form
Ethics Statement
To Appear
Editorial Login
Contacts
 
ISSN (electronic): 2640-7361
ISSN (print): 2220-5438
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