Duke Mathematical Journal

An effective Ratner equidistribution result for SL(2,R)R2

Andreas Strömbergsson

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Abstract

Let G=SL(2,R)R2 be the affine special linear group of the plane, and set Γ=SL(2,Z)Z2. We prove a polynomially effective asymptotic equidistribution result for the orbits of a 1-dimensional, nonhorospherical unipotent flow on Γ\G.

Article information

Source
Duke Math. J., Volume 164, Number 5 (2015), 843-902.

Dates
First available in Project Euclid: 7 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1428419274

Digital Object Identifier
doi:10.1215/00127094-2885873

Mathematical Reviews number (MathSciNet)
MR3332893

Zentralblatt MATH identifier
1351.37014

Subjects
Primary: 37A17: Homogeneous flows [See also 22Fxx]
Secondary: 37A45: Relations with number theory and harmonic analysis [See also 11Kxx] 11K60: Diophantine approximation [See also 11Jxx]

Keywords
effective equidistribution Ratner equidistribution unipotent flow horocycle

Citation

Strömbergsson, Andreas. An effective Ratner equidistribution result for $\operatorname{SL}(2,\mathbb{R})\ltimes\mathbb{R}^{2}$. Duke Math. J. 164 (2015), no. 5, 843--902. doi:10.1215/00127094-2885873. https://projecteuclid.org/euclid.dmj/1428419274


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