  For any compact orientable irreducible 3-manifold $N$ with empty or
incompressible toral boundary, the twisted $L^2$-torsion is a non-negative
function defined on the representation variety
$\operatorname{Hom}(\pi_1(N),\operatorname{SL}(n,\mathbb C))$. The paper shows
that if $N$ has infinite fundamental group, then the $L^2$-torsion function is
strictly positive. Moreover, this torsion function is continuous when
restricted to the subvariety of upper triangular representations.
