Ozeki Polynomials and Jacobi Forms

Abstract

A Jacobi polynomial was introduced by Ozeki. It corresponds to the codes over ${\mathbb{F}}_2$. Later, Bannai and Ozeki showed how to construct Jacobi forms with various index using a Jacobi polynomial corresponding to the binary codes. It generalizes Broué-Enguehard map. In this paper, we study Jacobi polynomial which corresponds to the codes over ${\mathbb{F}}_{2f}$. We show how to construct Jacobi forms with various index over the totally real field. This is one of extension of Broué-Enguehard map.