Eisenstein series for Siegel modular groups

DOI10.1007/BF01459520zbMath0786.11024MaRDI QIDQ1318150

Shin-ichiro Mizumoto

Publication date: 9 May 1994

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

Full work available at URL: https://eudml.org/doc/165149

zbMATH Keywords

Fourier expansionfunctional equationautomorphic \(L\)-functionsanalytic continuationRankin-Selberg convolutionEpstein zeta-functionsgrowth of derivatives of confluent hypergeometric functionsSiegel-type non-holomorphic Eisenstein seriesslowly increasing partial derivative

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Fourier coefficients of automorphic forms (11F30) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66)

Related Items

Differential operators, exact pullback formulas of Eisenstein series, and Laplace transforms, Note on Siegel-Eisenstein series of low weight, Explicit formulae of Siegel Eisenstein series, On integrality of Eisenstein liftings, Certain series attached to an even number of elliptic modular forms, Note on Siegel-Eisenstein series, Nearly holomorphic Eisenstein liftings, Yoshida lifts and Selmer groups, Congruences for Hecke eigenvalues of Siegel modular forms, On Dirichlet series and Petersson products for Siegel modular forms, A Dirichlet series attached to three Siegel modular forms, Special values of triple product \(L\)-functions and nearly holomorphic Eisenstein series, On the functional equation of singular series, Functional equations of real analytic Jacobi Eisenstein series, On the zeros of symmetric square \(L\)-functions, Wormholes and spectral statistics in the Narain ensemble, 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

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• On Eisenstein series
• Confluent hypergeometric functions on tube domains
• On the functional equations satisfied by Eisenstein series
• 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. II: Functional equation
• Dirichlet series in the theory of Siegel modular forms
• L-functions attached to Jacobi forms of degree n. Part I. The basic identity.
• Die analytische Fortsetzung der Eisensteinreihe zur Siegelschen Modulgruppe.
• EISENSTEIN SERIES ON THE SYMPLECTIC GROUP
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