Higher torsion zeta functions (Q1842220)

The author studies a formula due to Ray and Singer, which expresses the holomorphic torsion of a Riemannian surface of genus \(\geq 2\) as a special value for the zeta function of a dynamical system. Similar formulas are proved by Fried for manifolds of constant negative curvature, and by Moscovici and Stanton for manifolds whose universal cover is homogeneous of fundamental rank one. Here these results are extended to the case of arbitrary locally homogeneous manifolds of odd dimension satisfying some additional conditions.