  We propose a definition for analytic torsion of the contact complex on
contact manifolds. We show it coincides with Ray-Singer torsion on any
3-dimensional CR Seifert manifold equipped with a unitary representation. In
this particular case we compute it and relate it to dynamical properties of the
Reeb flow. In fact the whole spectral torsion function we consider may be
interpreted on CR Seifert manifolds as a purely dynamical function through
Selberg-type trace formulae.
