There are three types of parabolic subgroups in $Sp(2,\mathbf{R})$. In this paper we show that the Eisenstein series with respect to the Siegel parabolic subgroup corresponds to the Eisenstein series with respect to the Jacobi parabolic subgroup by theta correspondences.
@article{1201012598,
author = {Niwa, Shinji},
title = {On theta correspondences for Eisenstein series},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {83},
number = {1},
year = {2007},
pages = { 161-166},
language = {en},
url = {http://dml.mathdoc.fr/item/1201012598}
}
Niwa, Shinji. On theta correspondences for Eisenstein series. Proc. Japan Acad. Ser. A Math. Sci., Tome 83 (2007) no. 1, pp. 161-166. http://gdmltest.u-ga.fr/item/1201012598/