A Selberg Trace Formula for GL3(Fp)∖GL3(Fq)/K
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Abstract
jats:pIn 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).</jats:p>
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Peer reviewed: True
Acknowledgements: We would like to thank the Fields Institute for organizing the Fields Undergraduate Summer Research Program in 2021. Daksh Aggarwal, Jiyuan Lu, Balazs Németh, and C. Shijia Yu were participants in this program while working on this paper. The project was proposed and supervised by Masoud Khalkhali and Asghar Ghorbanpour.
Publication status: Published
Funder: Fields Institute through the Fields Undergraduate Summer Research Program in 2021
Funder: Natural Sciences and Engineering Research Council of Canada
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2075-1680
