Vol. 8, No. 3, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Volume 12, Issue 3
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 4
Volume 11, Issue 3
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 4
Volume 10, Issue 3
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Older Issues
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 2-3
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 1-2
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 3-4
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
founded and published with the
scientific support and advice of
mathematicians from the
Moscow Institute of
Physics and Technology
 
ISSN (electronic): 2640-7361
ISSN (print): 2220-5438
Author Index
To Appear
 
Other MSP Journals
On products of shifts in arbitrary fields

Audie Warren

Vol. 8 (2019), No. 3, 247–261
Abstract

We adapt the approach of Rudnev, Shakan, and Shkredov (2018) to prove that in an arbitrary field F, for all A F finite with |A| < p14 if p := Char(F) is positive, we have

|A(A + 1)| |A|119 (log|A|)76,|AA| + |(A + 1)(A + 1)| |A|119 (log|A|)76.

This improves upon the exponent of 6 5 given by an incidence theorem of Stevens and de Zeeuw.

Keywords
growth, sum-product estimates, energy
Mathematical Subject Classification 2010
Primary: 11B75, 68R05
Milestones
Received: 6 December 2018
Revised: 30 April 2019
Accepted: 14 May 2019
Published: 23 July 2019
Authors
Audie Warren
Johann Radon Institute for Computational and Applied Mathematics
Linz
Austria