The generalized Whittaker functions for $SU(2,1)$ and the Fourier expansion of automorphic forms
The generalized Whittaker functions for $SU(2,1)$ and the Fourier expansion of automorphic forms
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$SU(2,1)$ 的广义 Whittaker 函数和自守形式的傅里叶展开
DOI：
10.3792/pjaa.76.55
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发表时间：
1999
影响因子：
1.7
通讯作者：
Yoshihiro Ishikawa
中科院分区：
文献类型：
--
作者：
Yoshihiro Ishikawa
自同构形式的傅里叶展开式的显式形式在理论中占有重要地位。本文研究了SU（2,1）的情况，给出了群的标准表示的广义Whittaker函数的显式公式。结合（K-O）的结果，我们得到了属于任意标准表示的自同构形式的完全展开的傅里叶展开式。
Explicit form of Fourier expansion of automorphic forms plays an important role in the theory. Here we investigate the case of SU(2, 1) and give an explicit formula of generalized Whittaker functions for the standard representations of the group. Together with a result of (K-O), we obtain a form of fully developed Fourier expansion of automorphic forms belonging to arbitrary standard representations.