Disappearance of cusp forms in special families

DOI10.2307/2946582zbMath0826.11024OpenAlexW2078020359MaRDI QIDQ1327597

Scott A. Wolpert

Publication date: 28 November 1995

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2946582

zbMATH Keywords

Riemann surfacesperturbationLaplace operatornewformpseudo-Laplacianhyperbolic structurespecial values of \(L\)-functionsasymptotic perturbation theorycuspidal eigenvaluesdisappearance of cusp formsoldformopening nodespinching collarRanking-Selberg \(L\)- function

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Perturbations of PDEs on manifolds; asymptotics (58J37)

Related Items (21)

Intrinsic Sound of Anti-de Sitter Manifolds ⋮ Dissolving a cusp form in the presence of multiplicities ⋮ Deformations of Maass forms ⋮ DISSOLVING OF CUSP FORMS: HIGHER‐ORDER FERMI'S GOLDEN RULES ⋮ Poincaré series for non-Riemannian locally symmetric spaces ⋮ Hyperbolic triangles without embedded eigenvalues ⋮ Grafting hyperbolic metrics and Eisenstein series ⋮ Spectral Convergence for Degenerating Sequences of Three Dimensional Hyperbolic Manifolds ⋮ Variation of Laplace spectra of compact ``nearly hyperbolic surfaces ⋮ Degeneration of Pseudo-Laplace Operators for Hyperbolic Riemann Surfaces ⋮ On the Existence of Maass Cusp Forms on Hyperbolic Surfaces with Cone Points ⋮ On the nonvanishing of Rankin-Selberg \(L\)-functions ⋮ Spectral theory of Laplacians for Hecke groups with primitive character ⋮ On Selberg's small eigenvalue conjecture and residual eigenvalues ⋮ Spectra of hyperbolic surfaces ⋮ Harmonic differentials and infinite geodesic joining two punctures on a Riemann surface ⋮ Cusps and the family hyperbolic metric ⋮ Relationship between the discrete and resonance spectrum for the Laplace operator on a noncompact hyperbolic Riemann surface ⋮ The asymptotic behavior of the Takhtajan-Zograf metric ⋮ Riemann’s zeta function and beyond ⋮ A Numerical Study of Eigenvalues of the Hyperbolic Laplacian for Polyhedra with One Cusp

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