An arithmetic of Hermitian modular forms of degree two
An arithmetic of Hermitian modular forms of degree two
复制标题
埃尔米特二阶模形式的算术
DOI：
10.1007/bf01399502
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发表时间：
1982
影响因子：
3.1
通讯作者：
H. Kojima
中科院分区：
文献类型：
--
作者：
H. Kojima
最近，在文献[11-13]中，Maass对Saito-Kurokawa关于Siegel模尖点型的猜想的研究提出了一些重要的思想。关于Saito-Kurokawa猜想的研究，我们也可以参考文献[2，6，10]和[20].本文将讨论关于F2（！~）的Hermitian模尖点形式的Maass结果的一个类比，其中F2（~）是与~= Z+ iZ相关联的二次埃尔米特模群。我们解释每个部分的内容。预备部分是W1。在W中，我们引入了由厄米特模形式组成的空间Jik（F2（~）），其在无穷远处的傅里叶展开的系数满足适当的关系，并且还引入了与Weil表示相关联的θ级数（cf. (2.1)和（2.2））。应用θ级数的变换公式，我们将建立J//k（F ~ 2（~））到
Recently, in [11-13], Maass has proposed some important ideas to the investigations of Saito-Kurokawa's conjecture about Siegel modular cusp forms of degree two. We may also refer to [2, 6, 10] and [20] for the studies of Saito-Kurokawa's conjecture.In this paper, we shall discuss an analogy of Maass's results in the case of Hermitian modular cusp forms with respect to F2 (!~), where F2 (~) is the Hermitian modular group of degree two associated with~= Z+ iZ. We explain the contents of each section. The preparatory section is w 1. In w we introduce the space JIk (F2 (~)) consisting of Hermitian modular forms whose coefficients of the Fourier expansion at infinity satisfy suitable relations and introduce also theta series associated with the Weil representation (cf.(2.1) and (2.2)). In w applying transformation formulas of theta series, we shall establish the existence of an injective mapping/'of J//k (F2 (~)) into