On the logarithmic derivative of zeta functions for compact   even-dimensional locally symmetric spaces
  We derive approximate formulas for the logarithmic de- rivative of the Selberg and Ruelle zeta functions over compact, even- dimensional, locally symmetric spaces of rank one. The obtained for- mulas are given in terms of the zeta-singularities. 
Muharem Avdispahic and Dzenan Gusic
math.NT