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$p$-ADIC 
$L$-FUNCTIONS FOR ORDINARY FAMILIES ON SYMPLECTIC GROUPS
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 
$\operatorname{Sp}(2n)_{/\mathbb{Q}}\times \operatorname{Sp}(2n)_{/\mathbb{Q}}$.
