Degenerate Eisenstein series for symplectic groups (Q2786990)

In this paper, the author considers the degenerate Eisenstein series associated to representations induced from a character of the Siegel maximal parabolic subgroup of symplectic groups over \(\mathbb{Q}\). The author determines the poles in the right half plane with their orders, the image of the Eisenstein series, and automorphic realizations of certain irreducible global representations. The location and orders of such poles have already been studied in the work of \textit{S. S. Kudla} and \textit{S. Rallis} [Ann. Math. (2) 140, No. 1, 1--80 (1994; Zbl 0818.11024)]. The author of this paper employs different techniques by analyzing in detail all the features appearing in the constant term of Eisenstein series, giving direct descriptions of the images of the Eisenstein series. The author expects to generalize the method and the result to the non-Siegel case.