Arithmetic expressions of Selberg's zeta functions for congruence subgroups
Representation Theory
2008-07-01 v8 Number Theory
Abstract
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.
Cite
@article{arxiv.math/0409101,
title = {Arithmetic expressions of Selberg's zeta functions for congruence subgroups},
author = {Yasufumi Hashimoto},
journal= {arXiv preprint arXiv:math/0409101},
year = {2008}
}
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12 pages