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arXiv · 2101.07675

Mahler measure of $P_d$ polynomials

Mahya Mehrabdollahei
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Abstract

This article investigates the Mahler measure of a family of 2-variate polynomials, denoted by $P_d, d\geq 1$, unbounded in both degree and genus. By using a closed formula for the Mahler measure introduced in "Volume function and Mahler measure of exact polynomials" (by Guilloux and March\'e), we are able to compute $m(P_d)$, for arbitrary $d$, as a sum of the values of dilogarithm at special roots of unity. We prove that $m(P_d)$ converges and the limit is proportional to $\zeta(3)$, where $\zeta$ is the Riemann zeta function.

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Mahya Mehrabdollahei. 2021-01-18. Mahler measure of $P_d$ polynomials. https://arxiv.org/abs/2101.07675

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