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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01986598
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Submitted on : Friday, January 18, 2019 - 8:21:57 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM

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

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