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arXiv · 1106.1304

Higher Mahler measure for cyclotomic polynomials and Lehmer's question

Matilde Lalín·Kaneenika Sinha
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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.

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Matilde Lalín, Kaneenika Sinha. 2011-06-07. Higher Mahler measure for cyclotomic polynomials and Lehmer's question. https://arxiv.org/abs/1106.1304

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