An Eichler-Zagier map for Jacobi forms of half-integral weight (Q2382018)

In the paper under review the authors construct the Eichler-Zagier map which is a Hecke-invariant map from the space of Jacobi cusp forms of half-integral weight \(k+\frac12\) on \(\Gamma_0(4M)\), index \(m\) and character \(\chi\) into a certain subspace of cusp forms of weight \(k\) on \(\Gamma_1(16m^2M)\). Moreover they show that there exists no Hecke-equivariant map from Jacobi forms of index 1 to index \(p\) (prime), whenever the weight is half-integral.