Selberg's zeta functions for congruence subgroups of modular groups in SL(2,R) and SL(2,C)

Abstract

It is known that the Selberg zeta function for the modular group has an expression in terms of the class numbers and the fundamental units of the indefinite binary quadratic forms. In the present paper, we generalize such a expression to any congruence subgroup of the modular groups in SL(2,R) and SL(2,C).