Spectral Estimates for Compact Hyperbolic Space Forms and the Selberg Zeta Function for $p$-Spectra II

Let G be a properly discontinuous group of orientation preserving isometries of the n-dimensional hyperbolic space H5 of constant curvature —1 without fixed points (with the exception of the identity map id) with compact fundamental domain. We consider the related Killing-Hopf space form V = H5/g. Let fl be the set of non-trivial free homotopy classes of V. In every class w E fi there lies exactly one dosed geodesic line. We denote by 1(w) and v(w) its length and muliplicity, respectively. The parallel displacement along a closed geodesic line induces an isometry of the tangent space in every point of that geodesic line with the eigenvalues 01 (w),. . . ,/35_ i (w), 1 with I/3(w)I = 1 (i = 1,..., n 1). Let e(w) be the p1h elementary symmetric function of the ,(w) (i = 1,... ,n 1), and put eo(w) = 1. Further on, we introduce the weight