The Zeta Mahler measure of $(z^n − 1)/(z − 1)$

Arunabha Biswas (1) , M Ram Murty (2)

1 Department of Mathematics Univ. North Texas
2 Department of Mathematics and Statistics, Queen’s University

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.

Mots clés: Mahler measure; higher Mahler measure 2010 Mathematics Subject Classification 11R06; 11M99

Domaines: Mathématiques [math]; Théorie des nombres [math.NT]

Arunabha Biswas, M Ram Murty. The Zeta Mahler measure of $(z^n − 1)/(z − 1)$. Hardy-Ramanujan Journal, 2019, Atelier Digit_Hum, pp.77 - 84. ⟨10.46298/hrj.2019.5109⟩. ⟨hal-01986598⟩