A Note on Eigenvalues of Hecke Operators on Siegel Modular Forms of Degree Two

DOI10.2307/2048596zbMath0736.11025OpenAlexW4232933475MaRDI QIDQ3982120

Winfried Kohnen

Publication date: 26 June 1992

Full work available at URL: https://doi.org/10.2307/2048596

zbMATH Keywords

Dirichlet seriesMaass spaceabscissa of convergenceSiegel cusp formRamanujan-Petersson conjectureFourier Jacobi coefficient

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Hecke-Petersson operators, differential operators (several variables) (11F60)

Related Items

Arithmetic behaviour of Hecke eigenvalues of Siegel cusp forms of degree two, Estimating Hecke eigenvalues of Siegel modular forms, On the convergence of spinor zeta functions attached to Hecke eigenforms on \(Sp_ 4(\mathbb{Z} )\), On a convolution series attached to a Siegel Hecke cusp form of degree 2, Eigenform product identities for degree two Siegel modular forms, On the Petersson inner products of Fourier–Jacobi coefficients and Hecke eigenvalues of Siegel cusp forms

Cites Work

• The theory of Jacobi forms
• Über Kernfunktionen für Jacobiformen und Siegelsche Modulformen. (Kernel functions for Jacobi forms and Siegel modular forms)
• Das Vertauschungsgesetz zwischen Hecke-Operatoren und dem Siegelschen \(\Phi\) -Operator. (The commutation property between Hecke operators and Siegel's \(\Phi\) -operator)
• A certain Dirichlet series attached to Siegel modular forms of degree two
• On the poles of Andrianov L-functions
• THE ACTION OF MODULAR OPERATORS ON THE FOURIER-JACOBI COEFFICIENTS OF MODULAR FORMS
• Fourier coefficients of Siegel cusp forms of degree two
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