eng
episciences.org
Hardy-Ramanujan Journal
2804-7370
2019-01-23
10.46298/hrj.2019.5109
5109
journal article
The Zeta Mahler measure of $(z^n − 1)/(z − 1)$
Arunabha Biswas
M Ram Murty
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.
https://hrj.episciences.org/5109/pdf
Mahler measure
higher Mahler measure 2010 Mathematics Subject Classification 11R06
11M99
[ MATH ] Mathematics [math]
[ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT]