Soonki Hong

Vertex volumes, lattice-minima tails, and height zeta functions for the standard arithmetic quotient of $\operatorname{PGL}_d$

We study the standard nonuniform arithmetic quotient of the affine Bruhat--Tits building attached to $\operatorname{PGL}_d(\mathbb F_q(\!(t^{-1})\!))$, with Haar measure normalized so that a maximal compact subgroup has volume one. We first compute its vertex volume in closed product form. The proof is entirely buildin...