The Siegel operator and Hecke operators

DOI10.1007/BF01078595zbMath0314.10021OpenAlexW2073820912MaRDI QIDQ1220527

N. A. Zharkovskaya

Publication date: 1974

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01078595

zbMATH Keywords

Siegel modular formzeta-functioneigenfunction of all Hecke operators

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Other groups and their modular and automorphic forms (several variables) (11F55) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66)

Related Items (13)

Ein Rationalitätssatz für formale Heckereihen zur Siegelschen Modulgruppe. (A rationality theorem for formal Hecke series related to the Siegel modular group) ⋮ On automorphic forms on the unitary symplectic group \(\mathrm{Sp}(n)\) and \(\mathrm{SL}_ 2(\mathbb R)\) ⋮ The Hecke-algebras related to the unimodular and modular group over the Hurwitz order of integral quaternions ⋮ Local densities of quadratic forms and Fourier coefficients of Eisenstein series ⋮ The rationality of holomorphic Eisenstein series ⋮ On Eisenstein series for Siegel modular groups ⋮ Algebraicity of metaplectic \(L\)-functions ⋮ Poles and residues of standard L-functions attached to Siegel modular forms ⋮ Continuation of Siegel modular forms to the Siegel-Satake semiplane ⋮ Eigenform product identities for degree two Siegel modular forms ⋮ Trace operator and theta series ⋮ Das Vertauschungsgesetz zwischen Hecke-Operatoren und dem Siegelschen \(\Phi\) -Operator. (The commutation property between Hecke operators and Siegel's \(\Phi\) -operator) ⋮ The Siegel-Jacobi operator

Cites Work

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• Modular forms of degree \(n\) and representation by quadratic forms
• Theory of spherical functions on reductive algebraic groups over p-adic fields
• Die Primzahlen in der Theorie der Siegelschen Modulfunktionen. (The prime numbers in the theory of Siegel's modular functions)
• SPHERICAL FUNCTIONS FORGL_nOVER LOCAL FIELDS, AND SUMMATION OF HECKE SERIES
• ON MODULAR CORRESPONDENCES FOR SP(N, Z ) AND THEIR CONGRUENCE RELATIONS

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