Limiting value of higher Mahler measure

Abstract

We consider the $k$-higher Mahler measure $m_k(P)$ of a Laurent polynomial $P$ as the integral of ${\log }^k\left|P\right|$ over the complex unit circle. In this paper we derive an explicit formula for the value of $\left|m_k(P)\right|/k!$ as $k\to \infty .$

5 pages