A Selberg Trace Formula for GL₃(\mathbbF_p)\backslash GL₃(\mathbbF_q)/K

2023/01/04 by Daksh Aggarwal, Aggarwal, Daksh, Asghar Ghorbanpour +9
Biochemistry, Genetics and Molecular Biology · Mathematics · #11F72 #Advanced Algebra and Geometry #Amino Acid Enzymes and Metabolism #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2301.01654

openalex publication_date 2023/01/04 · openalex created_date 2023/01/08 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove a discrete analog of the Selberg Trace Formula for the group GL₃(\mathbbF_q). By considering a cubic extension of the finite field \mathbbF_q, we define an analog of the upper half space and an action of GL₃(\mathbbF_q) 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= Ind_Γ^G 1 for G= GL₃(\mathbbF_q) and Γ= GL₃(\mathbbF_p).

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