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Journal Articles Hardy-Ramanujan Journal Year : 2019

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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Dates and versions

hal-01986598 , version 1 (18-01-2019)

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Cite

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⟩

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