Some remarks on metaplectic cusp forms and the correspondences of Shimura and Waldspurger

DOI10.1007/BF02760615zbMath0526.10026OpenAlexW2014886110MaRDI QIDQ594918

Ilya I. Piatetski-Shapiro, Stephen Gelbart

Publication date: 1983

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02760615

zbMATH Keywords

cuspidal automorphic representationautomorphic representationstrong multiplicity one theoremmetaplectic coveringsuse of L- functionsweak multiplicity one theorem

Mathematics Subject Classification ID

(p)-adic theory, local fields (11F85) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Zeta functions and (L)-functions (11S40) Langlands-Weil conjectures, nonabelian class field theory (11S37)

Related Items (11)

Base change for \(SL_ 2^{\sim}\) ⋮ On Hilbert modular forms of half-integral weight ⋮ On the metaplectic analog of Kazhdan's ``endoscopic lifting ⋮ On Whittaker models and the vanishing of Fourier coefficients of cusp forms ⋮ On the nonvanishing of some \(L\)-functions ⋮ Toric Periods and 𝑝-adic Families of Modular Forms of Half-Integral Weight ⋮ Some results in the theory of genuine representations of the metaplectic double cover of \(GSp_{2n}(F)\) over \(p\)-adic fields ⋮ On Base Change for Odd Orthogonal Groups ⋮ Special representations of rank one orthogonal groups ⋮ Waldspurger’s involution and lifting of characters ⋮ On the Saito-Kurokawa lifting

Cites Work

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• Some examples of automorphic forms on Sp4
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• Sur les coefficients de Fourier des formes modulaires de poids demi-entier
• Uniqueness and existence of Whittaker models for the metaplectic group
• Weil's representation and the spectrum of the metaplectic group
• Shimura and Shintani correspondences
• Sur certains groupes d'opérateurs unitaires
• Automorphic forms on GL (2)
• On modular forms of half integral weight
• L-Indistinguishability For SL (2)
• Modular forms of half integral weight and the integral of certain theta-functions
• Interwining Operators and Automorphic Forms for the Metaplectic Group
• On construction of holomorphic cusp forms of half integral weight

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