## Biswas , Arunabha and Murty , M Ram - The Zeta Mahler measure of $(z^n − 1)/(z − 1)$

hrj:5109 - Hardy-Ramanujan Journal, January 23, 2019
The Zeta Mahler measure of $(z^n − 1)/(z − 1)$

Authors: Biswas , Arunabha and Murty , M Ram

We consider the k-higher Mahler measure $m_k (P)$ of a Laurent polynomial $P$ as the integral of ${\log}^k |P |$ over the complex unit circle and zeta Mahler measure as the generating function of the sequence ${m_k (P)}$. In this paper we derive a few properties of the zeta Mahler measure of the polynomial $P_n (z) := (z^N − 1)/(z − 1)$ and propose a conjecture.

Source : oai:HAL:hal-01986598v1
Published on: January 23, 2019
Submitted on: January 23, 2019
Keywords: Mahler measure,higher Mahler measure 2010 Mathematics Subject Classification 11R06,11M99, [ MATH ] Mathematics [math], [ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT]