On the Fourier expansions of Jacobi forms of half-integral weight (Q2644143)

Recently, \textit{H.~Skogman} [Int. J. Math. Math. Sci. 2004, No. 45--48, 2583--2594 (2004; Zbl 1116.11031), Ramanujan J. 10, No. 3, 325--339 (2005; Zbl 1154.11320)] showed that when certain components of a vector-valued modular form associated to a Jacobi form of weight \(k\) and index \(m\) are zero, then some of the other components must be zero, when \(m\) is a square-free positive integer. In this article, the authors generalize the work of Skogman to Jacobi forms of half-integral weight. Namely, they obtain the number of components which determine the given Jacobi form of index \(p\), \(p^2\) or \(pq\), where \(p\) and \(q\) are odd primes.