Theta correspondence for Eisenstein series
The authors study the theta correspondence between automorphic forms on the symplectic and the split orthogonal group. Their main interest is the lifting of Eisenstein series between these groups. Since the usual integral against a theta kernel does not converge in this case they have to apply a suitable differential operator to it to make the integral converge. The results allow to connect the (Klingen-) Eisenstein series on the symplectic group formed with respect to the different maximal parabolic subgroups with the standard Eisenstein series on the split orthogonal group of varying size (and vice versa). This gives new proofs of functional equation and analytic continuation as well as information about poles and residues and a Kronecker limit formula for the Eisenstein series on the orthogonal group.
scientific article; zbMATH DE number 59947
scientific article