Arithmetic forms of Selberg zeta functions with applications to prime geodesic theorem

DOI10.3792/pjaa.78.120zbMath1027.11065OpenAlexW2029135115MaRDI QIDQ1869650

Maki Nakasuji, Tsuneo Arakawa, Shin-ya Koyama

Publication date: 14 January 2004

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.78.120

zbMATH Keywords

Selberg zeta-functionprime geodesic theoremdivision indefinite quaternion algebranumber of primitive hyperbolic conjugacy classes

Mathematics Subject Classification ID

Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (4)

Square integrals of the logarithmic derivatives of Selberg’s zeta functions in the critical strip ⋮ Euler products of Selberg zeta functions in the critical strip ⋮ Arithmetic expressions of Selberg's zeta functions for congruence subgroups ⋮ Universality of the Selberg zeta-function forthe modular group

Cites Work

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• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• The dimension of the space of cusp forms on the Siegel upper half plane of degree two related to a quaternion unitary group
• A spectral correspondence for Maaß waveforms
• On discontinuous groups operating on the product of the upper half planes
• Prime geodesic theorem.
• Zur Zahlentheorie der Quaternionen-Algebren.
• Class numbers of indefinite binary quadratic forms

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