Correspondence among Eisenstein series \(E_{2,1}(\tau,z),H_{3\over 2}(\tau)\) and \(E_ 2(\tau)\) (Q1360936)

The classical monograph by \textit{M. Eichler} and \textit{D. Zagier} [The theory of Jacobi forms, Prog. Math. 55 (1985; Zbl 0554.10018)] describes in great detail the correspondences between the space \(J_{k,1}\) of Jacobi forms of weight \(k\) and index 1, Kohnen's ``+'' space \({\mathcal M}_{k-1/2} (\Gamma_0(4))\) and the space \({\mathcal M}_{2k-2} (\Gamma)\) of elliptic modular forms. The paper under review refers to the case \(k=2\) and to the attached Eisenstein series, which are no longer absolutely convergent. In this case one has to apply the Hecke trick in order to obtain similar results. Moreover the correspondences are studied for non-holomorphic Eisenstein series.