Vol. 6, No. 4, 2013

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 4, 543–722
Issue 3, 363–541
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-4184 (online)
ISSN 1944-4176 (print)
 
Author index
To appear
 
Other MSP journals
An elementary inequality about the Mahler measure

Konstantin Stulov and Rongwei Yang

Vol. 6 (2013), No. 4, 393–397
Abstract

Let p(z) be a degree n polynomial with zeros zj,j = 1,2,,n. The total distance from the zeros of p to the unit circle is defined as td(p) = j=1n||zj| 1|. We show that up to scalar multiples, td(p) sits between M(p) 1 and m(p). This leads to an equivalent statement of Lehmer’s problem in terms of td(p). The proof is elementary.

Keywords
Mahler measure, total distance
Mathematical Subject Classification 2010
Primary: 11CXX
Milestones
Received: 9 July 2012
Revised: 12 February 2013
Accepted: 16 February 2013
Published: 8 October 2013

Communicated by Andrew Granville
Authors
Konstantin Stulov
Institute for Computational and Mathematical Engineering
Stanford University
Stanford, NY 94305
United States
Rongwei Yang
Department of Mathematics and Statistics
University of Albany
State University of New York
Albany, NY 12047
United States