Abstract
In this chapter, we want to discuss an integral representation for the standard L-function of degree n holomorphic Siegel cusp forms twisted by characters. The goal is to assume as little as possible about the Siegel modular forms. We will allow vector-valued modular forms with respect to any congruence subgroup. Rallis, Piatetski-Shapiro, and also Bocherer, have obtained the integral representation in special cases. We will modify their methods to suit our level of generality. We will illustrate an application of the integral representation to algebraicity of special values of the L-function in the genus 2 case.
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