The skew-Maass lift I: The case of harmonic Maass-Jacobi forms
Journal article, 2019

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.

Real-analytic Siegel modular forms

11F50

Maass-Siegel forms

Kohnen limit process

Secondary 11F30

Saito-Kurokawa lift

Primary 11F46

Maass lift of harmonic Maass-Jacobi forms

Author

Martin Raum

Chalmers, Mathematical Sciences, Algebra and geometry

University of Gothenburg

Olav K. Richter

University of North Texas

RESEARCH IN THE MATHEMATICAL SCIENCES

2522-0144 (ISSN) 2197-9847 (eISSN)

Vol. 6 2 22

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

Roots

Basic sciences

DOI

10.1007/s40687-019-0184-2

More information

Latest update

2/8/2021 1