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2013 An elementary inequality about the Mahler measure
Konstantin Stulov, Rongwei Yang
Involve 6(4): 393-397 (2013). DOI: 10.2140/involve.2013.6.393

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.

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Konstantin Stulov. Rongwei Yang. "An elementary inequality about the Mahler measure." Involve 6 (4) 393 - 397, 2013. https://doi.org/10.2140/involve.2013.6.393

Information

Received: 9 July 2012; Revised: 12 February 2013; Accepted: 16 February 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1327.11077
MathSciNet: MR3115974
Digital Object Identifier: 10.2140/involve.2013.6.393

Subjects:
Primary: 11Cxx

Rights: Copyright © 2013 Mathematical Sciences Publishers

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Vol.6 • No. 4 • 2013
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