Anton Deitmar
Geometric Zeta Functions, $L^2$-Theory, and Compact Shimura Manifolds
MSRI #1995-028

We define geometric zeta functions for locally symmetric spaces as  
generalizations of the zeta functions of Ruelle and Selberg.
As a special value at zero we obtain the Reidemeister torsion of the  
manifold. For hermitian spaces these zeta functions have as special  
value the quotient of the holomorphic torsion of Ray and Singer and  
the holomorphic $L^2$-torsion, where the latter is defined via the  
$L^2$-theory of Atiyah. For higher fundamental rank twisted torsion  
numbers appear.