The skew-Maass lift I The case of harmonic Maass–Jacobi forms

• Published in: Research in the mathematical sciences Vol. 6; no. 2
• Main Authors: Raum, Martin, Richter, Olav K.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 2019
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Kohnen limit process; Maass lift of harmonic Maass–Jacobi forms; Maass–Siegel forms; Mathematics; Mathematics and Statistics; Real-analytic Siegel modular forms; Saito–Kurokawa lift; Saito–Kurokawa lift; Primary 11F46; Secondary 11F30; Maass lift of harmonic Maass–Jacobi forms; 11F50; Real-analytic Siegel modular forms; Kohnen limit process; Maass–Siegel forms
• ISSN: 2522-0144; 2197-9847; 2197-9847
• DOI: 10.1007/s40687-019-0184-2

The classical Maass lift is a map from holomorphic Jacobi forms to holomorphic scalar-valued Siegel modular forms. Automorphic representation theory predicts a non-holomorphic and vector-valued analogue for Hecke eigenforms. This paper is the first part of a series of papers. In this series of papers, we provide an explicit construction of the non-holomorphic Maass lift that is linear and also applies to non-eigenforms. In this first part, we develop new techniques to study Fourier series expansions of Siegel modular forms, which allow us to construct a Maass lift from harmonic Maass–Jacobi forms to scalar-valued Maass–Siegel forms.