Asymptotic formulas for partial sums of class numbers of indefinite binary quadratic forms

Abstract

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.

14 pages. This paper has been withdrawn by the author since the main results are included in arXiv:1003.3716

References in corpus (2)

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

Cited by in corpus (2)

• Asymptotic evaluation of a function defined by power series
• Asymptotic expansion of a function defined by power series