  This paper is a continuation of our work on theta and zeta functions In the
previous papers we considered the case of even dimensional rank one symmetric
spaces of non-compact type. The present is concerned with the odd-dimensional
case, i.e. with odd-dimensional real hyperbolic manifolds. It is the natural
appearence of eta invariants in connection with super theta and zeta functions
what makes this case particularly interesting. (authors name corrected)
