  Let l be a link of d components. For every finite-index lattice in Z^d there
is an associated finite abelian cover of S^3 branched over l. We show that the
order of the torsion subgroup of the first homology of these covers has
exponential growth rate equal to the logarithmic Mahler measure of the
Alexander polynomial of l, provided this polynomial is nonzero. Our proof uses
a theorem of Lind, Schmidt and Ward on the growth rate of connected components
of periodic points for algebraic Z^d-actions.
