Theta and zeta functions for odd-dimensional locally symmetric spaces of   rank one
  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) 
Ulrich Bunke and Martin Olbrich