Jacobi Maaß forms (Q1032521)

The author introduces a new notion of non-holomorphic Jacobi Maaß forms of weight \(k\in\mathbb{Z}\) and index \(m\in \mathbb{N}\) as eigenfunctions of a certain differential operator. The well-known holomorphic, skew-holomorphic and real analytic Eisenstein series fit under this definition. Now examples of a cuspidal Jacobi Maaß form \(F_f\) of even weight \(k\) and index 1 associated with a Maaß form \(f\) for \(\Gamma_0(4)\) and weight \(k-1/2\) are constructed. The map \(f \mapsto F_f \) is Hecke equivariant and compatible with the representation theory of the Jacobi group.