A Selberg Trace Formula for GL3( )/K

In this paper, we prove a discrete analog of the Selberg Trace Formula for the group GL3( F q). By considering a cubic extension of the finite field F q , we define an analog of the upper half-space and an action of GL3( F 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=IndΓG1 for G=GL3( F q) and Γ=GL3( F p).