On Eisenstein series for the Hermitian modular groups and the Jacobi groups
type: Item
instance of: scholarly article
title: On Eisenstein series for the Hermitian modular groups and the Jacobi groups
zbMATH Open document ID: 0778.11029
DOI: 10.1007/BF02941621
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1993-08-31T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11F55
Mathematics Subject Classification ID: 11F30
zbMATH DE Number: 404311
zbMATH Keywords: Hermitian modular forms
zbMATH Keywords: Jacobi forms
zbMATH Keywords: meromorphic continuation
zbMATH Keywords: functional equation
zbMATH Keywords: Hermitian Eisenstein series of degree 2
zbMATH Keywords: explicit formula
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: Eisenstein series
zbMATH Keywords: Hermitian Jacobi modular group
author: Shoyu Nagaoka
reviewed by: Aloys Krieg
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 404311