Pairs in discrete lattice orbits with applications to Veech surfaces

Claire Burrin, Samantha Fairchild, Jon Chaika

Let ${\Lambda }_1$, ${\Lambda }_2$ be two discrete orbits under the linear action of a lattice $\Gamma <{\mathrm{SL}}_2(\mathbb{R})$ on the Euclidean plane. We prove a Siegel$-$Veech-type integral formula f…