The Mahler measure of a family of polynomials with arbitrarily many variables

Abstract

We present an exact formula for the Mahler measure of an infinite family of polynomials with arbitrarily many variables. The formula is obtained by manipulating the integral defining the Mahler measure using certain transformations, followed by an iterative process that reduces this computation to the evaluation of certain polylogarithm functions at sixth roots of unity. This yields values of the Riemann zeta function and the Dirichlet $L$-function associated to the character of conductor 3.