On the Shimura correspondence for \(GSp(4)\)

DOI10.1007/BF01459242zbMath0713.11034MaRDI QIDQ749581

Shek-Tung Wong, Solomon Friedberg

Publication date: 1991

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

Full work available at URL: https://eudml.org/doc/164815

zbMATH Keywords

theta seriesHecke operatorsmetaplectic automorphic formNovodvorsky's integral for the Rankin-Selberg convolutionShimura correspondent

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Theta series; Weil representation; theta correspondences (11F27) Other groups and their modular and automorphic forms (several variables) (11F55) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Hecke-Petersson operators, differential operators (several variables) (11F60)

Cites Work

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• The L and \(\gamma\) factors for generic representations of GSp(4,k)\(\times GL(2,k)\) over a local nonarchimedean field k
• Eisenstein series on the metaplectic group and nonvanishing theorems for automorphic L-functions and their derivatives
• Some Euler products associated with cubic metaplectic forms on GL(3)
• On Shimura's correspondence
• Local Shimura correspondence
• \(p\)-adic Whittaker functions on the metaplectic group
• Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
• Sur certains groupes d'opérateurs unitaires
• On modular forms of half integral weight
• L-functions attached to Jacobi forms of degree n. Part I. The basic identity.
• Modular forms of half integral weight and the integral of certain theta-functions
• On construction of holomorphic cusp forms of half integral weight
• A cubic analogue of the theta series.
• Ein arithmetischer Satz über eine Matrizengruppe.

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