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We compute higher moments of the Siegel–Veech transform over quotients of SL by the Hecke triangle groups. After fixing a normalization of the Haar measure on SL we use geometric results and linear algebra to create explicit integration formulas which give information about densities of -tuples of vectors in discrete subsets of which arise as orbits of Hecke triangle groups. This generalizes work of W. Schmidt on the variance of the Siegel transform over SLSL.
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Samantha Fairchild, A higher moment formula for the Siegel–Veech transform over quotients by Hecke triangle groups. Groups Geom. Dyn. 15 (2021), no. 1, pp. 57–81DOI 10.4171/GGD/591