Counting saddle connections in a homology class modulo q

2018/09/03 by Magee, Michael, Rühr, Rene, Gutiérrez-Romo, Rodolfo
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1809.00579

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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• Lengths of saddle connections on random translation surfaces of large genus
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