Hyperbolic Eisenstein series for geometrically finite hyperbolic surfaces of infinite volume

DOI10.4171/PRIMS/58-2-4zbMath1492.30089arXiv1201.3492OpenAlexW1562614859WikidataQ115481567 ScholiaQ115481567MaRDI QIDQ2135408

Thérèse Falliero

Publication date: 6 May 2022

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.3492

zbMATH Keywords

Eisenstein seriesharmonic differentialdegenerating surfaces

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Global Riemannian geometry, including pinching (53C20) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Automorphic forms, one variable (11F12) Automorphic forms in several complex variables (32N10) Differentials on Riemann surfaces (30F30)

Cites Work

• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• Holomorphic factorization of determinants of Laplacians on Riemann surfaces and a higher genus generalization of Kronecker's first limit formula
• On the wave representation of hyperbolic, elliptic, and parabolic Eisenstein series
• On the appearance of Eisenstein series through degeneration
• Harmonic differentials and closed geodesics on a Riemann surface
• Spectral limits for hyperbolic surfaces. II
• The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
• Spectral degeneration of hyperboloc Riemann surfaces
• The asymptotic behavior of Eisenstein series and a comparison of the Weil-Petersson and the Zograf-Takhtajan metrics
• Theta functions on Riemann surfaces
• On the spectral expansion of hyperbolic Eisenstein series
• Degeneracy of hyperbolic Eisenstein series
• On the resolvent of the Laplacian on functions for degenerating surfaces of finite geometry
• Die Resolvente zum Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. II
• Asymptotics of degenerating Eisenstein series
• Fourier coefficients of the resolvent for a Fuchsian group.
• Harmonic differentials and infinite geodesic joining two punctures on a Riemann surface
• Regular 𝑏-groups, degenerating Riemann surfaces, and spectral theory
• Spectral theory of infinite-area hyperbolic surfaces
• Resolvente zum Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. I
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item