The Dirichlet series of Koecher and Maaß and modular forms of weight 3/2
The Dirichlet series of Koecher and Maaß and modular forms of weight 3/2
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Koecher 和 Maaß 的狄利克雷级数以及权重 3/2 的模块化形式
DOI：
10.1007/bf02570834
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发表时间：
1992
影响因子：
0.8
通讯作者：
R. Schulze
中科院分区：
文献类型：
--
作者：
S. Böcherer;R. Schulze
模形式的基本问题是哪些模形式可以表示为 theta 级数的线性组合的问题，为了使这个问题有意义，我们当然必须指定应考虑哪种类型的 theta 级数。我们希望在这里遵循（在特殊情况下）所采取的方法，例如在 [B61, W a l l 中，其（以其一般形式）询问“对于群 FoC，哪个（尖头）模形式 F 的次数为 n 且权重为 k”）（N）可以表示为阶数为 m = 2 k 的积分二次形式的 n 次 theta 级数和相同级别 N 的线性组合？此外，人们希望根据 F 与所涉及的 theta 级数的 Petersson 内积来导出这种线性组合的显式表达式。这个问题的表示理论版本是问：adelic 辛（或metaplectic）群的哪个（尖头）自守表示
The basis problem for modular forms is the question which modular forms can be expressed as linear combinations of theta series, in order that this question makes sense one has of course to specify which type of theta series should be taken into account. We want here to follow (in a special case) the approach taken e.g. in [B61, W a l l which (in its general form) asks" Which (cuspidal) modular forms F of degree n and weight k for the group FoC")(N) can be expressed as linear combinations of the theta series of degree n of integral quadratic forms of rank m = 2 k and the same level N? Moreover, one wants to derive an explicit expression for such a linear combination in terms of the Petersson inner products of F with the theta series involved. The representation theoretic version of this question is to ask: Which (cuspidat) automorphic representations of the adelic symplectic (or metaplectic) group