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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Ordinary families of Klingen Eisenstein series on symplectic groups


Author: Zheng Liu
Journal: Trans. Amer. Math. Soc. 374 (2021), 3331-3395
MSC (2020): Primary 11F33; Secondary 11F30, 11F46, 11G18
DOI: https://doi.org/10.1090/tran/8270
Published electronically: February 24, 2021
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Abstract: We construct $ (n+1)$-variable Hida families of Klingen Eisenstein series on $ \operatorname {Sp}(2n+2)$ for $ n$-variable Hida families on $ \operatorname {Sp}(2n)$, and relate their images under the Siegel operator to $ p$-adic $ L$-functions. We also carry out some preliminary calculations of the non-degenerate Fourier coefficients of the constructed Klingen Eisenstein families.


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Additional Information

Zheng Liu
Affiliation: Department of Mathematics, University of California Santa Barbara, South Hall, Room 6512, Santa Barbara, California 93106

DOI: https://doi.org/10.1090/tran/8270
Received by editor(s): July 8, 2019
Received by editor(s) in revised form: February 24, 2020, July 10, 2020, and July 27, 2020
Published electronically: February 24, 2021
Additional Notes: During her time at IAS, the author was supported by the NSF under Grant No. DMS-1638352.
Article copyright: © Copyright 2021 American Mathematical Society