Ozeki polynomials and Jacobi forms

Abstract

A Jacobi polynomial was introduced by Ozeki. It corresponds to the codes over 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 Broue-Enguehard map. In this paper, we study Jacobi polynomial which corresponds to the codes over F-2f. We show how to construct Jacobi forms with various index over the totally real field. This is one of extension of Broue-Enguehard map.