  We propose a definition for analytic torsion of the Rumin complex on contact
manifolds. This is given by the derivative at zero of a well-chosen combination
of zeta functions of a fourth-order modified Rumin Laplacian. The regular value
at zero (before differentiation) of this well-chosen combination of zeta
functions is shown to be a contact invariant. The variation of our analytic
torsion is given as the integral of local terms, together with a global term
coming from the null-space of the Laplacian.
