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

Technion - Israel Institute of Technology, Tel Aviv University

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

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

Keywords

Counting asymptotics
Effective Ergodic Theorem
Saddle connections
Translation surfaces

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.aim.2019.106890

Cite this

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title = "Effective counting on translation surfaces",

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(T2−κ). We also provide effective versions of counting in sectors and in ellipses.",

keywords = "Counting asymptotics, Effective Ergodic Theorem, Saddle connections, Translation surfaces",

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N2 - 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.

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.

KW - Counting asymptotics

KW - Effective Ergodic Theorem

KW - Saddle connections

KW - Translation surfaces

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U2 - 10.1016/j.aim.2019.106890

DO - 10.1016/j.aim.2019.106890

M3 - مقالة

SN - 0001-8708

VL - 360

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 106890

ER -

Effective counting on translation surfaces

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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