JournalsggdVol. 15, No. 1pp. 57–81

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

  • Samantha Fairchild

    University of Washington, Seattle, USA
A higher moment formula for the Siegel–Veech transform over quotients by Hecke triangle groups cover
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Abstract

We compute higher moments of the Siegel–Veech transform over quotients of SL(2,R)(2,\mathbb{R}) by the Hecke triangle groups. After fixing a normalization of the Haar measure on SL(2,R)(2,\mathbb{R}) we use geometric results and linear algebra to create explicit integration formulas which give information about densities of kk-tuples of vectors in discrete subsets of R2\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,R)/(2,\mathbb{R})/SL(2,Z)(2,\mathbb{Z}).

Cite this article

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. 57–81

DOI 10.4171/GGD/591