A Jacobi theta series and its transformation laws

Abstract

We consider a generalization of Jacobi theta series and show that every such function is a quasi-Jacobi form. Under certain conditions we establish transformation laws for these functions with respect to the Jacobi group and prove such functions are Jacobi forms. In establishing these results, we construct other functions which are also Jacobi forms. These results are motivated by applications in the theory of vertex operator algebras. © 2014 World Scientific Publishing Company.