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

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