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arXiv · 1406.5135

Asymptotic nature of higher Mahler measure

Arunabha Biswas
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Abstract

We consider Akatsuka's zeta Mahler measure as a generating function of higher Mahler measure $m_k(P)$ of a polynomial $P,$ where $m_k(P)$ is the integral of $\log^{k}\left| P \right|$ over the complex unit circle. Restricting ourselves to $\displaystyle P(x)=x+r$ with $|r|=1$ we show some new asymptotic results regarding $m_k(P)$, especially $\left| m_k(P) \right|/k! \to 1/π$ as $k \to \infty.$

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Arunabha Biswas. 2014-08-22. Asymptotic nature of higher Mahler measure. https://arxiv.org/abs/1406.5135

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