Theta lifting from elliptic cusp forms to automorphic forms on <Emphasis Type="Italic">Sp</Emphasis>(1, <Emphasis Type="Italic">q</Emphasis>) |
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Authors: | Hiro-aki Narita |
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Institution: | (1) Osaka City University Advanced Mathematical Institute, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan |
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Abstract: | Tsuneo Arakawa formulated a theta lifting from elliptic cusp forms to automorphic forms on Sp(1,q) in his unpublished note, which was inspired by “Kudla lifting”, i.e. a theta lifting from elliptic modular forms to holomorphic
automorphic forms on SU(1,q). We prove that the images of Arakawa’s theta lifting belong to the space of bounded automorphic forms generating quaternionic
discrete series, which are non-holomorphic forms. In the appendix we provide the construction of Eisenstein series and Poincaré series generating such discrete series.
The author was partially supported by JSPS Research Fellowships for Young Scientist for April 2002 to March 2005. The results
of this paper were obtained in this period. |
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Keywords: | Real symplectic group of signature (1+ q− ) Quaternionic discrete series representation Weil representation Theta lifting Eisenstein– Poincaré series |
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