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

2008/07/01 by Yasufumi Hashimoto, Hashimoto, Yasufumi · 1 citation
Mathematics · #11E41 (Primary) #11M36 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0807.0056

openalex publication_date 2008/07/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

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

Cited by

• Asymptotic expansion of a function defined by power series

Related

• Prime geodesic theorem for the modular group
• Ihara zeta functions and class numbers
• Large moments and extreme values of class numbers of indefinite binary quadratic forms
• Sums of Kloosterman sums in the prime geodesic theorem
• The Prime Geodesic Theorem and Bounds for Character Sums