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arXiv · 0908.0171

Higher Mahler measures and zeta functions

Nobushige Kurokawa·Matilde Lalin·Hiroyuki Ochiai
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Abstract

We consider a generalization of the Mahler measure of a multivariable polynomial $P$ as the integral of $\log^k|P|$ in the unit torus, as opposed to the classical definition with the integral of $\log|P|$. A zeta Mahler measure, involving the integral of $|P|^s$, is also considered. Specific examples are computed, yielding special values of zeta functions, Dirichlet $L$-functions, and polylogarithms.

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Nobushige Kurokawa, Matilde Lalin, Hiroyuki Ochiai. 2009-08-03. Higher Mahler measures and zeta functions. https://doi.org/10.4064/aa135-3-5

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