Arithmetic expressions of Selberg's zeta functions for congruence subgroups

Details Arithmetic expressions of Selberg's zeta functions for congruence subgroups Arithmetic expressions of Selberg's zeta functions for congruence subgroups

2004-09-07

arxiv.org/abs/math/0409101v8

Journal of Number Theory, Vol. 122 (2007), p.324-335.

Mathematics

Representation Theory

12 pages

Scientific paper

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.

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