Vol. 6, No. 4, 2013

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

Volume 11, 1 issue

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
Cover Page
Editorial Board
Editors’ Addresses
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
Author Index
Coming Soon
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
An elementary inequality about the Mahler measure

Konstantin Stulov and Rongwei Yang

Vol. 6 (2013), No. 4, 393–397

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.

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

Communicated by Andrew Granville
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