Limiting value of higher Mahler measure

Arunabha Biswas; Chris Monico

Limiting value of higher Mahler measure

Number Theory 2014-06-20 v1

Authors: Arunabha Biswas , Chris Monico

Abstract

We consider the $k$ -higher Mahler measure $m_k(P)$ of a Laurent polynomial $P$ as the integral of $\log ^k \left| P \right|$ over the complex unit circle. In this paper we derive an explicit formula for the value of $\left| m_k(P) \right|/k!$ as $k \to \infty.$

Keywords

Mahler measure Laurent polynomial limiting value complex unit circle explicit formula asymptotic analysis

Cite

@article{arxiv.1406.5138,
  title  = {Limiting value of higher Mahler measure},
  author = {Arunabha Biswas and Chris Monico},
  journal= {arXiv preprint arXiv:1406.5138},
  year   = {2014}
}

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5 pages

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