  In Sarnak's paper, it was proved that the Selberg zeta function for SL(2,Z)
is expressed in terms of the fundamental units and the class numbers of the
primitive indefinite binary quadratic forms. The aim of this paper is to obtain
similar arithmetic expressions of the logarithmic derivatives of the Selberg
zeta functions for congruence subgroups of SL(2,Z). As applications, we study
the Brun-Titchmarsh type prime geodesic theorem, the asymptotic behavior of the
sum of the class number.
