On the semi-classical zeta functions for negatively curved manifolds

For geodesic flows on negatively curved manifolds, we discuss about spectral properties of transfer operators and related analytic properties of the semi-classical zeta functions. In the case of surfaces with constant negative curvature, the semi-classical zeta function coincides with the so-called Selberg zeta function (up to translation) and therefore its zeros are described precisely in the classical result of Selberg in 1950's. We will discuss how the particular feature of the arrangement of zeros in such special cases can be generalized to the variable curvature case.