On Eisenstein series for the Hermitian modular groups and the Jacobi groups
Let \(K\) be an imaginary quadratic number field of class number 1. As an application of his earlier paper [Abh. Math. Semin. Univ. Hamb. 59, 235- 262 (1989; Zbl 0707.11036)] the author derives the meromorphic continuation and functional equation under \(s\to 4-2k-s\) of the Hermitian Eisenstein series of degree 2 and weight \(k\) attached to \(K\). This leads to an explicit formula for the Fourier coefficients of the Hermitian Eisenstein series just as obtained by the reviewer [Math. Ann. 289, 663- 681 (1991; Zbl 0713.11033)]. In the second part the author studies the Eisenstein series for the Hermitian Jacobi modular group acting on \(\mathbb{H}\times\mathbb{C}^ 2\) and derives the functional equation by calculating the Fourier expansion explicitly.
scientific article; zbMATH DE number 404311
scientific article