# Fourier coefficients of Jacobi forms over Cayley numbers

### Minking Eie

National Chung Cheng University, Chia-Yi, Taiwan

## Abstract

In this paper, we shall compute explicitly the Fourier coefficients of the Eisenstein series

which is a Jacobi form of weight $k$ and index $m$ defined on $H×C_{C}$, the product of the upper half-plane and Cayley numbers over the complex field $C$. The coefficient of $e_{2πi(nz+σ(t,w))}$ with $nm>N(t)$, has the form

Here $S_{p}$ is an elementary factor which depends only on $ν_{p}(m)$, $ν_{p}(t)$, $ν_{p}(n)$ and $ν_{p}(nm–N(t))$. Also $S_{p}=1$ for almost all $p$. Indeed, one has $S_{p}=1$ if $ν_{p}(m)=ν_{p}(nm–N(t))=0$. An explicit formula for $S_{p}$ will be given in details. In particular, these Fourier coefficients are rational numbers.

## Cite this article

Minking Eie, Fourier coefficients of Jacobi forms over Cayley numbers. Rev. Mat. Iberoam. 11 (1995), no. 1, pp. 125–142

DOI 10.4171/RMI/168