A Selberg Trace Formula for GL3(Fp)∖GL3(Fq)/K

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-04 DOI:10.3390/axioms13060381

Daksh Aggarwal, Asghar Ghorbanpour, M. Khalkhali, Jiyuan Lu, Balázs Németh, C. S. Yu

引用次数: 0

Abstract

In this paper, we prove a discrete analog of the Selberg Trace Formula for the group GL3(Fq). By considering a cubic extension of the finite field Fq, we define an analog of the upper half-space and an action of GL3(Fq) on it. To compute the orbital sums, we explicitly identify the double coset spaces and fundamental domains in our upper half space. To understand the spectral side of the trace formula, we decompose the induced representation ρ=IndΓG1 for G=GL3(Fq) and Γ=GL3(Fp).

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GL3(Fp)∖GL3(Fq)/K 的塞尔伯格轨迹公式

在本文中，我们证明了群 GL3(Fq) 的塞尔伯格踪迹公式的离散类比。通过考虑有限域 Fq 的立方扩展，我们定义了上半空间的类似物和 GL3(Fq) 对它的作用。为了计算轨道和，我们明确识别了上半空间中的双余弦空间和基域。为了理解迹公式的谱侧，我们分解了 G=GL3(Fq) 和 Γ=GL3(Fp) 的诱导表示 ρ=IndΓG1 。

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.