Arithmetic expressions of Selberg’s zeta functions for congruence subgroups

نویسنده

  • Yasufumi Hashimoto
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.

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تاریخ انتشار 2004