Prime Geodesic Theorem for the Picard manifold under the mean-Lindelöf hypothesis

DOI10.1515/FORM.2001.034zbMath1061.11024OpenAlexW2013991742MaRDI QIDQ2753165

Shin-ya Koyama

Publication date: 29 October 2001

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/form.2001.034

zbMATH Keywords

Picard groupRankin-Selberg \(L\)-functionprime geodesic theorem

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Other Dirichlet series and zeta functions (11M41) Gauss and Kloosterman sums; generalizations (11L05) 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 (8)

Prime geodesic theorem for the Picard manifold ⋮ The second moment for counting prime geodesics ⋮ Prime geodesic theorem via the explicit formula of \(\Psi\) for hyperbolic 3-manifolds ⋮ Second moment of the prime geodesic theorem for \(\mathrm{PSL}(2, \mathbb{Z}[i)\)] ⋮ On Kuznetsov-Bykovskii's formula of counting prime geodesics ⋮ 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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