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.

Saito–Kurokawa lift

Real-analytic Siegel modular forms

Maass lift of harmonic Maass–Jacobi forms

Kohnen limit process

Maass–Siegel forms


Martin Raum

Chalmers, Mathematical Sciences, Algebra and geometry

Olav K. Richter

University of North Texas

Research in Mathematical Sciences

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

Vol. 6 22

Siegel modulära genererande funktioner

Swedish Research Council (VR) (2015-04139), 2016-01-01 -- 2019-12-31.

Subject Categories

Algebra and Logic


Mathematical Analysis



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