论文标题
具有非独立曲折的矢量价值自动形态功能的傅立叶扩展
Fourier expansions of vector-valued automorphic functions with non-unitary twists
论文作者
论文摘要
我们提供了双曲线拉普拉曲板的矢量值征收征值的傅立叶膨胀，这些曲线是曲折的方向扭曲的周期性。有限维矢量空间的任何内态性可以给出扭曲。没有关于可逆性或单位性的假设。此类本本特征的示例包括fuchsian群体的矢量价值扭曲的自动形式。我们进一步提供了傅立叶系数的详细描述，并明确识别其每个成分，这密切取决于扭曲内态的特征值及其Jordan块的大小。此外，我们确定傅立叶系数的生长特性。
We provide Fourier expansions of vector-valued eigenfunctions of the hyperbolic Laplacian that are twist-periodic in a horocycle direction. The twist may be given by any endomorphism of a finite-dimensional vector space; no assumptions on invertibility or unitarity are made. Examples of such eigenfunctions include vector-valued twisted automorphic forms of Fuchsian groups. We further provide a detailed description of the Fourier coefficients and explicitly identify each of their constituents, which intimately depend on the eigenvalues of the twisting endomorphism and the size of its Jordan blocks. In addition, we determine the growth properties of the Fourier coefficients.
