Effective Ratner theorem for SL(2,R) n R2 and gaps in √n modulo 1

Tim Browning; Ilya Vinogradov

doi:10.1112/jlms/jdw025

Effective Ratner theorem for SL(2,R) n R2 and gaps in √n modulo 1

Tim Browning
, Ilya Vinogradov

Research output: Contribution to journal › Article (Academic Journal) › peer-review

12 Citations (Scopus)

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Abstract

Let G = SL(2, R) n R2 and Γ = SL(2, Z) n Z2. Building on recent work of
Strömbergsson we prove a rate of equidistribution for the orbits of a certain 1-dimensional unipotent flow of Γ\G, which projects to a closed horocycle in the unit tangent bundle to the modular surface. We use this to answer a question of Elkies and McMullen by making effective the convergence of the gap distribution of √
n mod 1.

Original language	English
Pages (from-to)	563-584
Number of pages	22
Journal	Journal of the London Mathematical Society
Volume	83
Issue number	4
Early online date	24 May 2016
DOIs	https://doi.org/10.1112/jlms/jdw025
Publication status	Published - 1 Oct 2016

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title = "Effective Ratner theorem for SL(2,R) n R2 and gaps in √n modulo 1",

abstract = "Let G = SL(2, R) n R2 and Γ = SL(2, Z) n Z2. Building on recent work of Str{\"o}mbergsson we prove a rate of equidistribution for the orbits of a certain 1-dimensional unipotent flow of Γ\textbackslash{}G, which projects to a closed horocycle in the unit tangent bundle to the modular surface. We use this to answer a question of Elkies and McMullen by making effective the convergence of the gap distribution of √ n mod 1. ",

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T1 - Effective Ratner theorem for SL(2,R) n R2 and gaps in √n modulo 1

AU - Browning, Tim

AU - Vinogradov, Ilya

PY - 2016/10/1

Y1 - 2016/10/1

N2 - Let G = SL(2, R) n R2 and Γ = SL(2, Z) n Z2. Building on recent work of Strömbergsson we prove a rate of equidistribution for the orbits of a certain 1-dimensional unipotent flow of Γ\G, which projects to a closed horocycle in the unit tangent bundle to the modular surface. We use this to answer a question of Elkies and McMullen by making effective the convergence of the gap distribution of √ n mod 1.

AB - Let G = SL(2, R) n R2 and Γ = SL(2, Z) n Z2. Building on recent work of Strömbergsson we prove a rate of equidistribution for the orbits of a certain 1-dimensional unipotent flow of Γ\G, which projects to a closed horocycle in the unit tangent bundle to the modular surface. We use this to answer a question of Elkies and McMullen by making effective the convergence of the gap distribution of √ n mod 1.

U2 - 10.1112/jlms/jdw025

DO - 10.1112/jlms/jdw025

M3 - Article (Academic Journal)

SN - 0024-6107

VL - 83

SP - 563

EP - 584

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 4

ER -

Effective Ratner theorem for SL(2,R) n R2 and gaps in √n modulo 1

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