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

2008/06/30 by Yasufumi Hashimoto, Hashimoto, Yasufumi · 1 citation
Mathematics · #11E41 (Secondary) #11M36 (Primary) #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11E41 #msc:11M36

paper · pdf · doi:10.48550/arxiv.0806.4829

12 pages. This paper has been withdrawn by the author due to several wrong descriptions

openalex publication_date 2008/06/30 · arxiv created 2015/02/09 · arxiv updated 2015/02/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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).

Cited by

• Asymptotic formulas for partial sums of class numbers of indefinite binary quadratic forms
• Distributions of length multiplicities for negatively curved locally symmetric Riemannian manifolds

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