Prime geodesic theorem via the explicit formula of \(\Psi\) for hyperbolic 3-manifolds

DOI10.3792/pjaa.77.130zbMath1028.11032OpenAlexW2091236617MaRDI QIDQ696374

Maki Nakasuji

Publication date: 12 September 2002

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.77.130

zbMATH Keywords

Selberg zeta-functionprime geodesic theoremhyperbolic three-manifold

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

Prime geodesic theorem for the Picard manifold ⋮ The second moment for counting prime geodesics ⋮ Prime geodesic theorem for higher-dimensional hyperbolic manifold ⋮ Second moment of the prime geodesic theorem for \(\mathrm{PSL}(2, \mathbb{Z}[i)\)] ⋮ Prime geodesic theorem in the 3-dimensional hyperbolic space ⋮ The second moment of symmetric square L-functions over Gaussian integers ⋮ The prime geodesic theorem for \(\mathrm{PSL}2(\mathbb{Z}[i)\) and spectral exponential sums]

Cites Work

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• The arithmetic and geometry of some hyperbolic three manifolds
• Determinants of Laplacians
• Spectral functions, special functions and the Selberg zeta function
• The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
• Prime Geodesic Theorem for the Picard manifold under the mean-Lindelöf hypothesis
• The Determinant of the Eisenstein Matrix and Hilbert Class Fields
• Determinant Expression of Selberg Zeta Functions. II

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