On Saito-Kurokawa lifting to cohomological Siegel modular forms

Abstract

We discuss a theta lifting from Open image in new window to O(3,2), which will produce a certain class of residual cohomological automorphic forms on the orthogonal group. We will show an explicit formula for their Fourier expansions, in which the constant terms may also occur, by using the Fourier coefficients of a half-integral weight cusp form, which is similar to the classical formula for the holomorphic Saito-Kurokawa lifting at finite places.