The Hecke correspondence for Jacobi forms over the Cayley numbers (Q1907284)

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 \(s\mapsto k- 4-s\).