Fourier expansions of vector-valued automorphic functions with non-unitary twists

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-12 DOI:10.4310/CNTP.2023.v17.n1.a5

Ksenia Fedosova, A. Pohl, J. Rowlett

引用次数: 1

Abstract

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.

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具有非幺正扭转的向量值自同构函数的傅里叶展开式

我们给出了在环方向上扭曲周期的双曲拉普拉斯向量值特征函数的傅里叶展开式。扭转可以由有限维向量空间的任何自同态给出;没有对可逆性或唯一性的假设。这种特征函数的例子包括Fuchsian群的向量值扭曲自同构形式。我们进一步提供了傅里叶系数的详细描述，并明确地确定了它们的每个组成部分，这些组成部分密切依赖于扭转自同态的特征值及其乔丹块的大小。此外，我们确定了傅里叶系数的增长特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.