Modular forms of varying weight. I

DOI10.1007/BF01214747zbMath0553.10021OpenAlexW4256364845MaRDI QIDQ801962

Roelof Wichert Bruggeman

Publication date: 1985

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

Full work available at URL: https://eudml.org/doc/173642

zbMATH Keywords

eigenvalueHilbert spacespectrumEisenstein seriesDedekind eta-functionPoincaré seriesorthonormal basisLaplacianmeromorphic continuationpseudo-Laplaciansquare integrable functionsFourier coefficientmultiplier system

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) General theory of partial differential operators (47F05) Holomorphic modular forms of integral weight (11F11)

Related Items (6)

The Eisenstein family for the modular group along closed geodesics ⋮ Construction of Poincaré-type Series by Generating Kernels ⋮ Linking numbers of modular geodesics ⋮ Cycle integrals of a sesqui-harmonic Maass form of weight zero ⋮ Computation of Maass waveforms with nontrivial multiplier systems ⋮ Modular forms of varying weight. II

Cites Work

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• Local analysis of Selberg's trace formula
• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• Fourier coefficients of automorphic forms
• Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. I, II. (The eigenvalue problem of automorphic forms in the hyperbolic plane. I. II)
• Ein Satz über ganzwertige Funktionen als Prinzip für Transzendenzbeweise
• Scattering Theory for Automorphic Functions. (AM-87)

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