Cusp forms for character varieties

DOI10.1007/BF01898362zbMath0804.11038WikidataQ101117833 ScholiaQ101117833MaRDI QIDQ1326537

Ralph S. Phillips, Peter C. Sarnak

Publication date: 22 January 1995

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/58158

zbMATH Keywords

perturbation theorySelberg trace formulaeigenvalues of Laplacianprincipal congruence subgroup\(L\)-functions attached to modular formsspace of cuspidal Maass forms

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Perturbation theory of linear operators (47A55) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Holomorphic modular forms of integral weight (11F11) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (8)

Dissolving a cusp form in the presence of multiplicities ⋮ The unbounded denominators conjecture for the noncongruence subgroups of index 7 ⋮ DISSOLVING OF CUSP FORMS: HIGHER‐ORDER FERMI'S GOLDEN RULES ⋮ Hyperbolic triangles without embedded eigenvalues ⋮ Noncongruence subgroups and Maass waveforms ⋮ Spectral theory of Laplacians for Hecke groups with primitive character ⋮ On Selberg's small eigenvalue conjecture and residual eigenvalues ⋮ Perturbation of Zeros of the Selberg Zeta Function for Γ₀(4)

Cites Work

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• On cusp forms for co-finite subgroups of PSL(2,\({\mathbb{R}})\)
• The spectrum of Fermat curves
• Spectral limits for hyperbolic surfaces. I
• Spectral limits for hyperbolic surfaces. II
• A non-vanishing theorem for zeta functions of \(\mathrm{GL}_n\)
• Maass cusp forms
• Cusp forms and Hecke groups.
• Perturbation Theory for the Laplacian on Automorphic Functions
• Scattering Theory for Automorphic Functions. (AM-87)
• Simple Zeros of the Riemann Zeta-Function on the Critical Line
• The weyl theorem and the deformation of discrete groups

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