Jacobi forms and discrete series representations of the Jacobi group

DOI10.1007/BF02570858zbMath0695.10024OpenAlexW1992476193MaRDI QIDQ909704

Siegfried Böcherer, Rolf Berndt

Publication date: 1990

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

Full work available at URL: https://eudml.org/doc/183795

zbMATH Keywords

Jacobi formsJacobi groupinvariant differential operatorsduality theoremdimensions of spaces of Jacobi cusp formsmultiplicities of discrete series representationsnon-reductive group

Mathematics Subject Classification ID

Other groups and their modular and automorphic forms (several variables) (11F55) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Jacobi forms (11F50)

Related Items (20)

ON THE GEOMETRY OF SIEGEL–JACOBI DOMAINS ⋮ \(L\)-functions for Jacobi forms à la Hecke ⋮ On local Whittaker models for the Jacobi group of degree one ⋮ On automorphic \(L\)-functions for the Jacobi group of degree one and a relation with \(L\)-functions for Jacobi forms ⋮ The continuous part of \(L^ 2(\Gamma ^ J\backslash G^ J)\) for the Jacobi group \(G^ J\) ⋮ On the characterization of skew-holomorphic Jacobi-forms ⋮ Invariant metric on the extended Siegel-Jacobi upper half space ⋮ Saito-Kurokawa liftings of level \(N\) and practical construction of Jacobi forms ⋮ Spherical representations of the Jacobi group ⋮ Centers and characters of Jacobi group-invariant differential operator algebras ⋮ A CONVENIENT COORDINATIZATION OF SIEGEL–JACOBI DOMAINS ⋮ CONSEQUENCES OF THE FUNDAMENTAL CONJECTURE FOR THE MOTION ON THE SIEGEL–JACOBI DISK ⋮ Coherent states and geometry on the Siegel–Jacobi disk ⋮ Balanced metric and Berezin quantization on the Siegel-Jacobi ball ⋮ Theta functions on Hermitian symmetric domains and fock representations ⋮ On Eisenstein series for the Hermitian modular groups and the Jacobi groups ⋮ A HOLOMORPHIC REPRESENTATION OF THE JACOBI ALGEBRA ⋮ Jacobi Maaß forms ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

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• The theory of Jacobi forms
• Unitary representations of group extensions. I
• A new class of modular forms and modular functions
• Jacobiformen und Thetareihen. (Jacobi forms and theta series)
• Die Jacobigruppe und die Wärmeleitungsgleichung. (The Jacobi group and the heat equation)
• Primitive vollprime Ideale in der Einhüllenden von \(\mathfrak {so}(5,\mathbb{C})\)
• Metrisierungstheorie und Jacobiformen. (Metrization theory and Jacobi forms)
• Siegel's modular forms and Dirichlet series. Course given at the University of Maryland, 1969-1970
• L-functions attached to Jacobi forms of degree n. Part I. The basic identity.
• Automorphic Forms on Adele Groups. (AM-83)

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