Geodesic
Asymptotic nature of higher Mahler measure
Arunabha Biswas 1
1 Department of Mathematics and Statistics Texas Tech University Broadway & Boston Lubbock, TX 79409-1042, U.S.A.
Acta Arithmetica, Tome 166 (2014) no. 1, pp. 15-21 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $k \rightarrow \infty .$
DOI : 10.4064/aa166-1-2
Keywords: consider akatsukas zeta mahler measure generating function higher mahler measure polynomial where integral log complex unit circle restricting ourselves x r asymptotic results regarding particular rightarrow rightarrow infty

Arunabha Biswas  1

1 Department of Mathematics and Statistics Texas Tech University Broadway & Boston Lubbock, TX 79409-1042, U.S.A. 
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Arunabha Biswas. Asymptotic nature of higher Mahler measure. Acta Arithmetica, Tome 166 (2014) no. 1, pp. 15-21. doi: 10.4064/aa166-1-2

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