Universite ́ des Sciences et de la technologie

In this paper, we study the Mahler measure of a family of reciprocal polynomials depending of a parameter l. These polynomials do not vanish on the torus and define curves of genus 1 except for the singular values of the parameter. Using Mahler measure, we prove that Picard-Fuchs equation associated to this family admits explicit solutions at ±∞ and express certain Dirichlet L-series L (χ, 2) as integrals of functions related to