The Hecke correspondence for Jacobi forms over the Cayley numbers
type: Item
instance of: scholarly article
title: The Hecke correspondence for Jacobi forms over the Cayley numbers
zbMATH Open document ID: 0844.11034
author: Minking Eie
published in: Southeast Asian Bulletin of Mathematics
publication date: 1996-09-01T00:00:00Z
review text: In an earlier paper [Trans. Am. Math. Soc. 342, 793-805 (1994)]\ the author and the reviewer had investigated the space \(J_{k,m}\) of Jacobi forms of weight \(k\) and index \(m\) over the Cayley numbers defined on \({\mathcal H}\times \mathbb{C}^8\). The space \(J_{k,m}\) turns out to be isomorphic to a space of vector valued elliptic modular forms of weight \(k-4\). In the paper under review the author uses the Hecke correspondence in order to obtain a correspondence between Jacobi forms and vector valued Dirichlet series with meromorphic continuation to the whole plane and a functional equation under \(s\mapsto k- 4-s\).
Mathematics Subject Classification ID: 11F66
Mathematics Subject Classification ID: 11F50
zbMATH DE Number: 846083
zbMATH Keywords: Cayley numbers
zbMATH Keywords: elliptic modular forms
zbMATH Keywords: Hecke correspondence
zbMATH Keywords: Jacobi forms
zbMATH Keywords: vector valued Dirichlet series
zbMATH Keywords: functional equation
reviewed by: Aloys Krieg
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 846083