Ordinary families of Klingen Eisenstein series on symplectic groups

Liu, Zheng

doi:10.1090/tran/8270

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
MathSciNet review: 4237950
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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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