Theta lifting from elliptic cusp forms to automorphic forms on \(\mathrm{Sp}(1, q)\)

DOI10.1007/s00209-007-0239-8zbMath1211.11056OpenAlexW2169109981MaRDI QIDQ926246

Hiro-aki Narita

Publication date: 27 May 2008

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

Full work available at URL: https://doi.org/10.1007/s00209-007-0239-8

zbMATH Keywords

theta liftingEisenstein-Poincaré seriesquaternionic discrete series representationreal symplectic group of signature (1+,q-)

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Other groups and their modular and automorphic forms (several variables) (11F55) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (5)

Realization of quaternionic discrete series on the unit ball in \(\mathbb H^d\) ⋮ Commutation relations of Hecke operators for Arakawa lifting ⋮ SOME VECTOR-VALUED SINGULAR AUTOMORPHIC FORMS ON U(2, 2) AND THEIR RESTRICTION TO Sp(1, 1) ⋮ Fourier expansion of Arakawa lifting. I: An explicit formula and examples of non-vanishing lifts ⋮ A quaternionic Saito-Kurokawa lift and cusp forms on \(G_2\)

Cites Work

• Fourier-Jacobi expansion of automorphic forms on \(\text{Sp}(1,q)\) generating quaternionic discrete series
• On certain arithmetic automorphic forms for SU(1,q)
• Fourier coefficients of modular forms on \(G_2\).
• Automorphic forms on semisimple Lie groups. Notes by J. G. M. Mars.
• Sur certains groupes d'opérateurs unitaires
• On modular forms of half integral weight
• On quaternionic discrete series representations, and their continuations.
• On construction of holomorphic cusp forms of half integral weight
• D 4 modular forms
• Lectures on Modular Forms. (AM-48)
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