Estimations on dimensions of spaces of Jacobi forms (Q1283090)

Siegel proved a theorem saying that a Siegel modular form \(f\) of genus \(n\) and weight \(k\) vanishes identically whenever the Fourier coefficients \(\alpha_f(T)\) vanish for \(\text{trace} (T)\leq k\kappa_n\). In the paper under review the author derives an analogous result for Jacobi cusp forms in the sense of Ziegler. This leads to estimates for the dimension of the space of Jacobi cusp forms even for congruence subgroups.