Arithmetic expressions of Selberg’s zeta functions for congruence subgroups
نویسنده
چکیده
Abstract In [Sa], it was proved that the Selberg zeta function for SL2(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 SL2(Z). As applications, we study the Brun-Titchmarsh type prime geodesic theorem, the asymptotic behavior of the sum of the class number.
منابع مشابه
Selberg ’ s zeta functions for congruence subgroups of modular groups in SL 2 ( R ) and SL 2 ( C ) Yasufumi Hashimoto
Sarnak gave an expressions of Selberg’s zeta function for the modular group in terms of the class numbers and the fundamental units of the indefinite binary quadratic forms. The main result of the present paper is the extension of his expression to the congruence subgroups of the modular groups in SL2(R) and SL2(C).
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