Effective counting on translation surfaces

Amos Nevo; Rene Rühr; Barak Weiss

doi:10.1016/j.aim.2019.106890

Effective counting on translation surfaces

Amos Nevo, Rene Rühr^*, Barak Weiss

^*Corresponding author for this work

School of Mathematical Sciences

Technion-Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We prove an effective version of a celebrated result of Eskin and Masur: for any SL₂(R)-invariant locus L of translation surfaces, there exists κ>0, such that for almost every translation surface in L, the number of saddle connections with holonomy vector of length at most T, grows like cT²+O(T^2−κ). We also provide effective versions of counting in sectors and in ellipses.

Original language	English
Article number	106890
Journal	Advances in Mathematics
Volume	360
DOIs	https://doi.org/10.1016/j.aim.2019.106890
State	Published - 22 Jan 2020

Funding

Funders	Funder number
ERC starter	DLGAPS 279893
Israel Science Foundation	2095/15
Stavros Niarchos Foundation	P2EZP2 168823

Keywords

Counting asymptotics
Effective Ergodic Theorem
Saddle connections
Translation surfaces

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10.1016/j.aim.2019.106890

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AB - We prove an effective version of a celebrated result of Eskin and Masur: for any SL2(R)-invariant locus L of translation surfaces, there exists κ>0, such that for almost every translation surface in L, the number of saddle connections with holonomy vector of length at most T, grows like cT2+O(T2−κ). We also provide effective versions of counting in sectors and in ellipses.

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KW - Effective Ergodic Theorem

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Effective counting on translation surfaces

Abstract

Funding

Keywords

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