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arXiv · 1901.10115

A higher moment formula for the Siegel--Veech transform over quotients by Hecke triangle groups

Samantha K. Fairchild
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Abstract

We compute higher moments of the Siegel--Veech transform over quotients of $SL(2,\mathbb{R})$ by the Hecke triangle groups. After fixing a normalization of the Haar measure on $SL(2,\mathbb{R})$ we use geometric results and linear algebra to create explicit integration formulas which give information about densities of $k$-tuples of vectors in discrete subsets of $\mathbb{R}^2$ which arise as orbits of Hecke triangle groups. This generalizes work of W.~Schmidt on the variance of the Siegel transform over $SL(2,\mathbb{R})/SL(2,\mathbb{Z})$.

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Samantha K. Fairchild. 2020-06-04. A higher moment formula for the Siegel--Veech transform over quotients by Hecke triangle groups. https://doi.org/10.4171/ggd%2F591

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