Involve: A Journal of Mathematics

  • Involve
  • Volume 6, Number 4 (2013), 393-397.

An elementary inequality about the Mahler measure

Konstantin Stulov and Rongwei Yang

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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.

Article information

Involve, Volume 6, Number 4 (2013), 393-397.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11CXX

Mahler measure total distance


Stulov, Konstantin; Yang, Rongwei. An elementary inequality about the Mahler measure. Involve 6 (2013), no. 4, 393--397. doi:10.2140/involve.2013.6.393.

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