Vol. 6, No. 4, 2013

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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