Selberg type zeta function for the Hilbert modular group of a real quadratic field

DOI10.3792/pjaa.88.145zbMath1305.11077OpenAlexW1990315052MaRDI QIDQ1949177

Yasuro Gon

Publication date: 25 April 2013

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

Full work available at URL: https://projecteuclid.org/euclid.pja/1352210375

zbMATH Keywords

Selberg zeta functionHilbert modular groupclass numbers of binary quadratic forms over ring of integersdifferences of Selberg trace formulasprime geodesic type theoremRuelle type zeta function

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)

Related Items (1)

Differences of the Selberg trace formula and Selberg type zeta functions for Hilbert modular surfaces

Cites Work

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• Differences of the Selberg trace formula and Selberg type zeta functions for Hilbert modular surfaces
• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• The zeta functions of Ruelle and Selberg for hyperbolic manifolds with cusps
• Selberg trace formula for the Hilbert modular group of a real quadratic algebraic number field
• The Selberg trace formula for 𝑃𝑆𝐿₂(𝑅)ⁿ
• Class numbers of indefinite binary quadratic forms

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