Arithmetic expressions of Selberg's zeta functions for congruence subgroups
Copyright policy )Arithmetic expressions of Selberg's zeta functions for congruence subgroups
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.
12 pages
- Kyushu University Japan
class number, Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), Algebra and Number Theory, prime geodesic theorem, Mathematics - Number Theory, Spectral theory; trace formulas (e.g., that of Selberg), 11M36, 11E41, 11F72, Class numbers of quadratic and Hermitian forms, Selberg's zeta function, Prime geodesic theorem, FOS: Mathematics, Number Theory (math.NT), Representation Theory (math.RT), Mathematics - Representation Theory, Class number
class number, Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), Algebra and Number Theory, prime geodesic theorem, Mathematics - Number Theory, Spectral theory; trace formulas (e.g., that of Selberg), 11M36, 11E41, 11F72, Class numbers of quadratic and Hermitian forms, Selberg's zeta function, Prime geodesic theorem, FOS: Mathematics, Number Theory (math.NT), Representation Theory (math.RT), Mathematics - Representation Theory, Class number
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