Poles and residues of standard L-functions attached to Siegel modular forms

DOI10.1007/BF01446591zbMath0713.11035OpenAlexW2092513976MaRDI QIDQ749582

Shin-ichiro Mizumoto

Publication date: 1991

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

Full work available at URL: https://eudml.org/doc/164800

zbMATH Keywords

automorphic formsholomorphic modular formHecke algebraSiegel modular groupsautomorphic L-functions

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items

The special values of the standard 𝐿-functions for 𝐺𝑆𝑝_{2𝑛}×𝐺𝐿₁, On algebraicity of vector valued Siegel modular forms, Nearly holomorphic Eisenstein liftings, Discrete series multiplicities for classical groups over \(\mathbb{Z}\) and level 1 algebraic cusp forms, Correction to: ``Poles and residues of standard \(L\)-functions attached to Siegel modular forms, Congruences to Ikeda-Miyawaki lifts and triple \(L\)-values of elliptic modular forms, Garrett's pullback formula for vector valued Siegel modular forms, A Dirichlet series attached to three Siegel modular forms, Ramanujan type congruences for the Klingen-Eisenstein series, On the standard \(L\)-function for \(\mathrm{GSp}_{2n}\times\mathrm{GL}_1\) and algebraicity of symmetric fourth \(L\)-values for \(\mathrm{GL}_2\), Siegel Modular Forms and Their Applications, PRIME DENSITY RESULTS FOR HECKE EIGENVALUES OF A SIEGEL CUSP FORM, Transfer of Siegel cusp forms of degree 2, Integral representation for \(L\)-functions for \(\text{GSp}_4\times \text{GL}_2\), Special values of L-functions for Saito–Kurokawa lifts, On special values of standard \(L\)-functions attached to vector valued Siegel modular forms., Congruences for Fourier coefficients of lifted Siegel modular forms. I: Eisenstein lifts

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Über die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen. II
• On the second L-functions attached to Hilbert modular forms
• On Eisenstein series
• Stabile Modulformen und Eisensteinreihen. (Stable modular forms and Eisenstein series)
• Harmonische Formen in einer Matrixvariablen. (Harmonic forms in one matrix variable)
• Thetareihen mit harmonischen Koeffizienten zur Siegelschen Modulgruppe
• On the poles of Andrianov L-functions
• On Siegel eigenforms
• The critical values of zeta functions associated to the symplectic group
• Über die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen
• The Siegel operator and Hecke operators
• Konstruktion von Spitzenformen beliebigen Grades mit Hilfe von Thetareihen. (Construction of cusp forms of arbitrary degree by means of Theta series)
• On the functional equations satisfied by Eisenstein series
• Zum Darstellungssatz für Siegelsche Modulformen
• Zur Begründung der Theorie der automorphen Funktionen in mehreren Variablen
• ON THE ANALYTIC PROPERTIES OF STANDARD ZETA FUNCTIONS OF SIEGEL MODULAR FORMS
• Über Funktionalgleichungen automorpher L-Funktionen zur Siegelschen Modulgruppe.
• Poles and residues of Eisenstein series for symplectic and unitary groups
• THE MULTIPLICATIVE ARITHMETIC OR SIEGEL MODULAR FORMS
• A CHARACTERIZATION OF THE MAASS SPACE OF SIEGEL CUSP FORMS OF SECOND DEGREE
• Special values of zeta functions attached to Siegel modular forms
• On the Holomorphy of Certain Dirichlet Series
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• Problems in the theory of automorphic forms to Salomon Bochner in gratitude