Arunabha Biswas ; M Ram Murty - The Zeta Mahler measure of $(z^n − 1)/(z − 1)$

hrj:5109 - Hardy-Ramanujan Journal, January 23, 2019 - https://doi.org/10.46298/hrj.2019.5109
The Zeta Mahler measure of $(z^n − 1)/(z − 1)$Article

Authors: 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.

https://doi.org/10.46298/hrj.2019.5109
Source: HAL:hal-01986598v1
Published on: January 23, 2019
Imported on: January 23, 2019
Keywords: Mahler measure,higher Mahler measure 2010 Mathematics Subject Classification 11R06,11M99, [ MATH ] Mathematics [math], [ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT]
Funding:
    Source : OpenAIRE Graph
  • Funder: Natural Sciences and Engineering Research Council of Canada

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