On sign changes of Jacobi forms

Abstract

In this paper, using two kinds of expansion of a Jacobi cusp form, we prove that there are infinitely many sign changes of Fourier coefficients of a Jacobi cusp form of real weight. We also give an explicit upper bound for the first sign change when the weight is an even integer, the index is a positive odd square-free integer and the group is the congruence subgroup of square-free level.