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$p$-ADIC 
$L$-FUNCTIONS FOR ORDINARY FAMILIES ON SYMPLECTIC GROUPS
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 19 / Issue 4 / July 2020
- Published online by Cambridge University Press:
- 14 January 2019, pp. 1287-1347
- Print publication:
- July 2020
-
- Article
- Export citation
-
We construct the
$p$-adic standard 
$L$-functions for ordinary families of Hecke eigensystems of the symplectic group 
$\operatorname{Sp}(2n)_{/\mathbb{Q}}$ using the doubling method. We explain a clear and simple strategy of choosing the local sections for the Siegel Eisenstein series on the doubling group 
$\operatorname{Sp}(4n)_{/\mathbb{Q}}$, which guarantees the nonvanishing of local zeta integrals and allows us to 
$p$-adically interpolate the restrictions of the Siegel Eisenstein series to 
$\operatorname{Sp}(2n)_{/\mathbb{Q}}\times \operatorname{Sp}(2n)_{/\mathbb{Q}}$.
