Mixed Siegel Modular Forms and Special Valuesof Certain Dirichlet Series

Abstract

Let \(\) be a Siegel modular form of weight ?, and let \(\) be an Eichler embedding, where \(\) denotes the Siegel upper half space of degree n. We use the notion of mixed Siegel modular forms to construct the linear map \(\) of the spaces of Siegel cusp forms for the congruence subgroup \(\) and express the Fourier coefficients of the image \(\) of an element \(\) under \(\) in terms of special values of a certain Dirichlet series. We also discuss connections between mixed Siegel cusp forms and holomorphic forms on a family of abelian varieties.