On the theory of Jacobi forms and Fourier-Jacobi coefficients of Eisenstein series. (English) Zbl 0822.11041
The Fourier-Jacobi expansion of the holomorphic Siegel-Eisenstein series was calculated by S. Böcherer [Math. Z. 183, 21-46 (1983; Zbl 0503.10018), ibid. 189, 81-110 (1985; Zbl 0558.10022)]. The Fourier-Jacobi coefficients turn out to be finite sums of products of theta functions and Eisenstein series.
In the paper under review the author deals with the analogous problem for the nonanalytic Eisenstein series on the symplectic and unitary group. In these cases the Fourier-Jacobi coefficients are no longer of the above type, but are infinitely approximable by them. Applications to the calculation of the residues of Eisenstein series are announced.
In the paper under review the author deals with the analogous problem for the nonanalytic Eisenstein series on the symplectic and unitary group. In these cases the Fourier-Jacobi coefficients are no longer of the above type, but are infinitely approximable by them. Applications to the calculation of the residues of Eisenstein series are announced.
Reviewer: A.Krieg (Aachen)
MSC:
| 11F50 | Jacobi forms |
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
