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

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 spac...

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Bibliographic Details
Published in:Axioms 2024-06, Vol.13 (6), p.381
Main Authors: Aggarwal, Daksh, Ghorbanpour, Asghar, Khalkhali, Masoud, Lu, Jiyuan, Németh, Balázs, Yu, C Shijia
Format: Article
Language:English
Subjects:
Fields (mathematics)
Fourier transforms
Graphs
Half spaces
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Summary: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).
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13060381