Hardy Ramanujan Journal |

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.

Source : oai:HAL:hal-01986598v1

Published on: January 23, 2019

Submitted on: January 23, 2019

Keywords: Mahler measure,higher Mahler measure 2010 Mathematics Subject Classification 11R06,11M99,
[
MATH
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Mathematics [math],
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MATH.MATH-NT
]
Mathematics [math]/Number Theory [math.NT]