A note on a hypercubic Mahler measure and associated Bessel Integral

TL;DR

This paper explores the Mahler measure of a specific polynomial, reducing it to a Bessel function integral, and examines special cases to deepen understanding of its properties.

Contribution

It introduces a novel reduction of the Mahler measure to a Bessel integral for a class of polynomials and analyzes several special cases.

Findings

Reduction of Mahler measure to Bessel integral for the polynomial

Explicit evaluation of special cases

Insights into the structure of Mahler measures

Abstract

The Mahler measure for the n-variable polynomial $k+\sum(x_j+1/x_j)$ is reduced to a single integral of the n-th power of the modified Bessel function $I_0$. Several special cases are examined in detail