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Transactions of the American Mathematical Society

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On the lifting of Hilbert cusp forms to Hilbert-Hermitian cusp forms


Author: Shunsuke Yamana
Journal: Trans. Amer. Math. Soc. 373 (2020), 5395-5438
MSC (2010): Primary 11F11, 11F30, 11F55; Secondary 11F27, 11F70
DOI: https://doi.org/10.1090/tran/8096
Published electronically: May 28, 2020
MathSciNet review: 4127881
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Abstract: We construct a lifting that associates to a Hilbert cusp form a Hilbert-Hermitian cusp form. This is a generalization of the lifting of elliptic cusp forms constructed by Ikeda to arbitrary Hilbert cusp forms.


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Additional Information

Shunsuke Yamana
Affiliation: Advanced Mathematical Institute, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585 Japan
MR Author ID: 871756
Email: yamana@sci.osaka-cu.ac.jp

Keywords: Hilbert cusp forms, Hermitian cusp forms, Duke-Imamoglu-Ikeda lifts, degenerate principal series, generalized Shalika model, Siegel series
Received by editor(s): May 7, 2019
Received by editor(s) in revised form: August 25, 2019
Published electronically: May 28, 2020
Additional Notes: The author is partially supported by JSPS Grant-in-Aid for Scientific Research (C) 18K03210 and (B) 19H01778
The author was partially supported by Osaka City University Advanced Mathematical Institute (MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics).
Article copyright: © Copyright 2020 American Mathematical Society