Kohnen’s limit process for real-analytic Siegel modular forms

AbstractKohnen introduced a limit process for Siegel modular forms that produces Jacobi forms. He asked if there is a space of real-analytic Siegel modular forms such that skew-holomorphic Jacobi forms arise via this limit process. In this paper, we initiate the study of harmonic skew-Maass–Jacobi forms and harmonic Siegel–Maass forms. We improve a result of Maass on the Fourier coefficients of harmonic Siegel–Maass forms, which allows us to establish a connection to harmonic skew-Maass–Jacobi forms. In particular, we answer Kohnen’s question in the affirmative