scientific article; zbMATH DE number 1207249

DOI10.1155/S1073792898000257zbMath0917.11019OpenAlexW36666398MaRDI QIDQ4212809

Shin-ya Koyama

Publication date: 20 July 1999

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/s1073792898000257

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zbMATH Keywords

Jacquet-Langlands correspondenceprime geodesic theoremfirst eigenvalue of the Laplacianarithmetic cocompact subgroup of \(\text{PSL} (2,\mathbb{R})\)

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (15)

Square integrals of the logarithmic derivatives of Selberg’s zeta functions in the critical strip ⋮ Gallagherian PGT on some compact Riemannian manifolds of negative curvature ⋮ Mean square in the prime geodesic theorem ⋮ Gallagherian \(PGT\) on \(\mathrm{PSL}(2,\mathbb{Z})\) ⋮ Euler products of Selberg zeta functions in the critical strip ⋮ Weighted prime geodesic theorems ⋮ ASYMPTOTIC FORMULAS FOR CLASS NUMBER SUMS OF INDEFINITE BINARY QUADRATIC FORMS ON ARITHMETIC PROGRESSIONS ⋮ A prime geodesic theorem for \(\mathrm{SL}_4\) ⋮ On von Koch theorem for \(\mathrm{PSL}(2,\mathbb{Z})\) ⋮ CM-points and lattice counting on arithmetic compact Riemann surfaces ⋮ A prime geodesic theorem for higher rank. II: Singular geodesics ⋮ Prime geodesic theorem in the 3-dimensional hyperbolic space ⋮ THE MEAN SQUARE OF THE LOGARITHMIC DERIVATIVE OF THE SELBERG ZETA FUNCTION FOR COCOMPACT DISCRETE SUBGROUPS ⋮ Effective bounds for Huber’s constant and Faltings’s delta function ⋮ Arithmetic forms of Selberg zeta functions with applications to prime geodesic theorem

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