On the spectral expansion of hyperbolic Eisenstein series

DOI10.1007/s00208-009-0422-9zbMath1251.30045OpenAlexW2021662974MaRDI QIDQ2267763

Jürg Kramer, Anna-Maria von Pippich, Jay A. Jorgenson

Publication date: 2 March 2010

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-009-0422-9

zbMATH Keywords

Eisenstein seriesspectral expansiongeodesicmeromorphic continuationfinite volume hyperbolic surface

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) 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) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (10)

Hyperbolic Eisenstein series for geometrically finite hyperbolic surfaces of infinite volume ⋮ Construction of Poincaré-type Series by Generating Kernels ⋮ Applications of Kronecker's limit formula for elliptic Eisenstein series ⋮ On the wave representation of hyperbolic, elliptic, and parabolic Eisenstein series ⋮ LOXODROMIC EISENSTEIN SERIES THROUGH DEGENERATION ⋮ On the appearance of Eisenstein series through degeneration ⋮ Kronecker limit formulas for parabolic, hyperbolic and elliptic Eisenstein series via Borcherds products ⋮ Loxodromic Eisenstein series for cofinite Kleinian groups ⋮ Hyperbolic Eisenstein series on \(n\)-dimensional hyperbolic spaces ⋮ Eisenstein series of even weight 𝑘≥2 and integral binary quadratic forms

Cites Work

• On the appearance of Eisenstein series through degeneration
• Unipotent vector bundles and higher-order non-holomorphic Eisenstein series
• Harmonic differentials and closed geodesics on a Riemann surface
• Asymptotics of the determinant of the Laplacian on hyperbolic surfaces of finite volume
• Convergence of the normalized spectral counting function on degenerating hyperbolic Riemann surfaces of finite volume
• Degeneracy of hyperbolic Eisenstein series
• Properties of Eisenstein series formed with modular symbols
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