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In this paper, we calculate the ramified local integrals in the doublingmethod and present an integral representation of standard $L$-functions forclassical groups. We explicitly construct local sections of Eisenstein seriessuch that the local ramified integrals represent certain ramified $L$-factors.As an application, we prove algebraicity of special $L$-values and construct$p$-adic $L$-functions for symplectic, unitary, quaternionic unitary andquaternionic orthogonal groups.

Algebracity and the $p$-adic Interpolation of Special $L$-values for certain Classical Groups