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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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Arunabha Biswas, M Ram Murty. The Zeta Mahler measure of $(z^n − 1)/(z − 1)$. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2019, 41, pp.77 - 84. ⟨hal-01986598⟩

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