Asymptotic nature of higher Mahler measure
Volume 166 / 2014
Acta Arithmetica 166 (2014), 15-21
MSC: 11R06, 11M99.
DOI: 10.4064/aa166-1-2
Abstract
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 $k \rightarrow \infty .$
