The $L^2$-torsion function and the Thurston norm of 3-manifolds

Let M be an oriented irreducible 3-manifold with infinite fundamental group and empty or toroidal boundary which is not S(1)x D-2. Consider any element phi in the first cohomology of M with integer coefficients. Then one can define the phi-twisted L-2-torsion function of the universal covering which is a function from the set of positive real numbers to the set of real numbers. By earlier work of the second author and Schick the evaluation at t = 1 determines the volume. In this paper we show that the degree of the L-2-torsion function, which is a number extracted from its asymptotic behavior at 0 and at infinity, agrees with the Thurston norm of phi