THE SPECIAL VALUES OF THE STANDARD L-FUNCTIONS FOR GSp(2n) x GL(1)

We prove the expected algebraicity property for the critical values of character twists of the standard L-function associated to vector-valued holomorphic Siegel cusp forms of archimedean type (k(1), k(2), ... , k(n)), where k(n) >= n + 1 and all k(i) are of the same parity. For the proof, we use an explicit integral representation to reduce to arithmetic properties of differential operators on vector-valued nearly holomorphic Siegel cusp forms. We establish these properties via a representation-theoretic approach.