Period functions and the Selberg zeta function for the modular group.

Abstract

this paper, is that the Selberg zeta function Z \\Gamma (s) of H=\\Gamma can be represented as the (Fredholm) determinant of the action of a certain element of the quotient field of the group ring Z[\\Gamma] on an appropriate Banach space. Specifically, let V be the space of functions holomorphic in D = fz 2 C j jz \\Gamma 1j !