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.

中文翻译：

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斜马斯电梯我

经典的Maass升力是从全同Jacobi形式到全同量标量Siegel模块化形式的映射。自纯表示理论预测了Hecke特征形的非全同和向量值类似物。本文是系列论文的第一部分。在这一系列论文中，我们提供了线性非线性全马氏提升的显式构造，并且也适用于非特征形式。在第一部分中，我们开发了新技术来研究Siegel模块化形式的Fourier级数展开，这使我们能够构造从调和Maass–Jacobi形式到标量值Maass–Siegel形式的Maass升力。