A Selberg Trace Formula for GL3(Fp)∖GL3(Fq)/K-Reference-Cited by-同舟云学术

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

Published:2024-06-04 Issue:6 Volume:13 Page:381
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Aggarwal Daksh¹,Ghorbanpour Asghar²^ORCID,Khalkhali Masoud²^ORCID,Lu Jiyuan³,Németh Balázs⁴^ORCID,Yu C Shijia³

Affiliation:

1. Department of Mathematics, Brown University, Providence, RI 02912, USA

2. Department of Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada

3. Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4, Canada

4. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK

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).

Funder

Fields Institute through the Fields Undergraduate Summer Research Program in 2021

Natural Sciences and Engineering Research Council of Canada

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/6/381/pdf

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