We construct the p-adic standard L-functions for ordinary families of Hecke eigen-systems of the symplectic group Sp(2n)=Q using the doubling method. We explain the strategy for choosing the local sections of the Siegel Eisenstein series on the doubling group Sp(4n)=Q, which allows p-adic interpolation and guarantees nonvanishing of the archimedean zeta integrals, and the corresponding local zeta integrals at p give the modied Euler factors at p as predicted by Coates for p-adic L-functions.

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