Half integral weight Jacobi forms and periods of modular forms

Abstract

By deriving Bol's type result, we show how to construct a Jacobi form with different weight from the given Jacobi form. We also show how this analogous theory related to the classical theory of Bol [1] by using the theta-series expansion of the Jacobi form. Furthermore. the partial converse of Bol's result involving the periods of modular forms reveals a connection between Jacobi forms and periods of modular forms.