Bounds for special values of Selberg zeta functions of Riemann surfaces

DOI10.1515/crll.2001.092zbMath0986.11058OpenAlexW2038960689MaRDI QIDQ2757778

Jürg Kramer, Jay A. Jorgenson

Publication date: 3 December 2001

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crll.2001.092

zbMATH Keywords

upper boundsRiemann surfaceshyperbolic Laplacianlower boundSelberg zeta functioncongruence subgroupslength spectrumsmall eigenvaluesconstant term of logarithmic derivative

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 (10)

An effective bound for the Huber constant for cofinite Fuchsian groups ⋮ Bounds on Faltings's delta function through covers ⋮ Arakelov self-intersection numbers of minimal regular models of modular curves \(X_0(p^2)\) ⋮ Effective bounds for Faltings's delta function ⋮ Self-intersection of the relative dualizing sheaf on modular curves \(X_{ 1 }(N)\) ⋮ On the appearance of Eisenstein series through degeneration ⋮ Bounds for canonical Green's function at cusps ⋮ Non-completeness of the Arakelov-induced metric on moduli space of curves ⋮ Effective bounds for Huber’s constant and Faltings’s delta function ⋮ Bounds for Green's functions on noncompact hyperbolic Riemann orbisurfaces of finite volume

Cites Work

• Basic analysis of regularized series and products
• Geometry and spectra of compact Riemann surfaces
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