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arXiv · 1810.06810

The skew-Maass lift I

Martin Raum·Olav K. Richter
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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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Martin Raum, Olav K. Richter. 2019-03-07. The skew-Maass lift I. https://arxiv.org/abs/1810.06810

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