Identities of Mahler measures of certain polynomials defining curves of arbitrary genus

Abstract The aim of this paper is to prove several Mahler measure identities involving families of two-variable polynomials defining curves of arbitrary genus. As an application, we also obtain the relation between the Mahler measure of non-tempered polynomials defining elliptic curves of conductor 14 , 15 , 24 , 48 , 54 and corresponding L-values.