JP Journal of Algebra, Number Theory and Applications
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Abstract: Boyd studied in [4] the Mahler measure of some families of
elliptic curves given by reciprocal polynomials depending on a real parameter l.
These curves are of genus 1 except for the singular values of the parameter l
and do not vanish on the torus for l
large enough.
Using the Mahler measure, we prove that the Picard-Fuchs
equation associated to one Boyd’s family admits explicit solutions at the
singularities of the equation and that we can express certain DirichletL-series as integrals of functions related to
the hypergeometric functions
