The edge zeta function of the standard non-uniform PGL3 quotient is computed exactly as a rational function, yielding an exact count of closed geodesic cycles.
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Edge zeta function and closed cycles in the standard non-uniform complex from $\operatorname{PGL}_3$
The edge zeta function of the standard non-uniform PGL3 quotient is computed exactly as a rational function, yielding an exact count of closed geodesic cycles.