Vol. 8, No. 2, 2019
Download this article
Download this article For screen
For printing
Recent Issues
Volume 13, Issue 4
Volume 13, Issue 3
Volume 13, Issue 2
Volume 13, Issue 1
Volume 12, Issue 4
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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
founded and published with the
scientific support and advice of
mathematicians from the
Moscow Institute of
Physics and Technology
Subscriptions
 
ISSN 2996-220X (online)
ISSN 2996-2196 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
A family of four-variable expanders with quadratic growth

Mehdi Makhul
Vol. 8 (2019), No. 2, 143–149
DOI: 10.2140/moscow.2019.8.143
Abstract

We prove that if g(x,y) is a polynomial of degree d that is not a polynomial of only y, then for any finite set A ⊂ ℝ

|X|≫d|A|2, where X :={g(a1,b1) − g(a2,b2) b2 − b1 : a1,a2,b1,b2 ∈ A}.

We will see this bound is also tight for some polynomial g(x,y).

PDF Access Denied

We have not been able to recognize your IP address 35.173.48.18 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
Bisector, expander functions
Mathematical Subject Classification 2010
Primary: 11B30
Secondary: 11B75
Milestones
Received: 11 May 2018
Revised: 17 July 2018
Accepted: 31 July 2018
Published: 20 May 2019
Authors
Mehdi Makhul
Johann Radon Institute for Computational and Applied Mathematics (RICAM)
Austrian Academy of Sciences, Linz and Research Institute for Symbolic Computation (RISC)
Johannes Kepler University
Linz
Austria