Asymptotic formulas for partial sums of class numbers of indefinite   binary quadratic forms
  Sarnak obtained the asymptotic formula of the sum of the class numbers of indefinite binary quadratic forms from the prime geodesic theorem for the modular group. In the present paper, we show several asymptotic formulas of partial sums of the class numbers by using the prime geodesic theorems for the congruence subgroups of the modular group. 
Yasufumi Hashimoto