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Asymptotic nature of higher Mahler measure

Volume 166 / 2014

Arunabha Biswas Acta Arithmetica 166 (2014), 15-21 MSC: 11R06, 11M99. DOI: 10.4064/aa166-1-2


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


  • Arunabha BiswasDepartment of Mathematics and Statistics
    Texas Tech University
    Broadway & Boston
    Lubbock, TX 79409-1042, U.S.A.

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