Meromorphic extensions of a class of zeta functions for two-dimensional billiards without eclipse

The main purpose of the present paper is to show that a class of dynamical zeta functions associated with the so-called two-dimensional open billiard without eclipse have meromorphic extensions to the half-plane consisting of all complex numbers whose real parts are greater than a certain negative number. As an application, we verify that the zeta function for the length spectrum of the corresponding billiard table has the same property.