$K$-spherical horospherical averages on the Nagao quotient: tree combinatorics and exact discrepancy

Sanghoon Kwon

Let \[ F=\mathbb{F}_q(\!(t^{-1})\!),\qquad G=\mathrm{SL}_2(F),\qquad Γ=\mathrm{SL}_2(\mathbb{F}_q[t]),\qquad X=Γ\backslash G, \] and let $K={\mathrm{SL}}_2(\mathcal{O})$, where $\m…