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Counting saddle connections in a homology class modulo \begin{document}$ \boldsymbol q $\end{document} (with an appendix by Rodolfo Gutiérrez-Romo)

Type of publication Peer-reviewed
Publikationsform Original article (peer-reviewed)
Author Magee Michael, Rühr Rene,
Project Application of Homogeneous Dynamics: Effective Equidistribution and Counting
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Original article (peer-reviewed)

Journal Journal of Modern Dynamics
Volume (Issue) 15(0)
Page(s) 237 - 262
Title of proceedings Journal of Modern Dynamics
DOI 10.3934/jmd.2019020

Open Access

URL https://arxiv.org/abs/1809.00579
Type of Open Access Repository (Green Open Access)

Abstract

We give effective estimates for the number of saddle connections on a translation surface that have length ≤L and are in a prescribed homology class modulo q. Our estimates apply to almost all translation surfaces in a stratum of the moduli space of translation surfaces, with respect to the Masur-Veech measure on the stratum.
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