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

T.D. Browning, I. Vinogradov, Journal of the London Mathematical Society 94 (2016) 61–84.

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Abstract
Let G = SL(2, R) ⋉R2 and Γ = SL(2, Z) ⋉Z2. Building on recent work of Strömbergsson, we prove a rate of equidistribution for the orbits of a certain one-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.
Publishing Year
Date Published
2016-05-24
Journal Title
Journal of the London Mathematical Society
Acknowledgement
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreements 291147 and 306457.
Volume
94
Issue
1
Page
61 - 84
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Browning TD, Vinogradov I. Effective ratner theorem for SL (2, R) ⋉R2 and gaps in √n modulo 1. Journal of the London Mathematical Society. 2016;94(1):61-84. doi:10.1112/jlms/jdw025
Browning, T. D., & Vinogradov, I. (2016). Effective ratner theorem for SL (2, R) ⋉R2 and gaps in √n modulo 1. Journal of the London Mathematical Society, 94(1), 61–84. https://doi.org/10.1112/jlms/jdw025
Browning, Timothy D, and Ilya Vinogradov. “Effective Ratner Theorem for SL (2, R) ⋉R2 and Gaps in √n modulo 1.” Journal of the London Mathematical Society 94, no. 1 (2016): 61–84. https://doi.org/10.1112/jlms/jdw025.
T. D. Browning and I. Vinogradov, “Effective ratner theorem for SL (2, R) ⋉R2 and gaps in √n modulo 1,” Journal of the London Mathematical Society, vol. 94, no. 1, pp. 61–84, 2016.
Browning TD, Vinogradov I. 2016. Effective ratner theorem for SL (2, R) ⋉R2 and gaps in √n modulo 1. Journal of the London Mathematical Society. 94(1), 61–84.
Browning, Timothy D., and Ilya Vinogradov. “Effective Ratner Theorem for SL (2, R) ⋉R2 and Gaps in √n modulo 1.” Journal of the London Mathematical Society, vol. 94, no. 1, John Wiley and Sons Ltd, 2016, pp. 61–84, doi:10.1112/jlms/jdw025.

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