Higher Mahler measure for cyclotomic polynomials and Lehmer's question

Matilde Lalín; Kaneenika Sinha

Higher Mahler measure for cyclotomic polynomials and Lehmer's question

Number Theory 2011-06-08 v1

Authors: Matilde Lalín , Kaneenika Sinha

Abstract

The $k$ -higher Mahler measure of a nonzero polynomial $P$ is the integral of $\log^k|P|$ on the unit circle. In this note, we consider Lehmer's question (which is a long-standing open problem for $k=1$ ) for $k>1$ and find some interesting formulae for 2- and 3-higher Mahler measure of cyclotomic polynomials.

Keywords

higher Mahler measure cyclotomic polynomial Lehmer's question unit circle logarithmic integral

Cite

@article{arxiv.1106.1304,
  title  = {Higher Mahler measure for cyclotomic polynomials and Lehmer's question},
  author = {Matilde Lalín and Kaneenika Sinha},
  journal= {arXiv preprint arXiv:1106.1304},
  year   = {2011}
}

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