The skew-Maass lift I

2018/10/16 by Raum, Martin, Richter, Olav K.
#11F30 #11F46 #11F50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1810.06810

Abstract

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.

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