Title: p-adic L-functions for Siegel modular forms

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