Effective Ratner Theorem for ASL(2, R) and the gaps of the sequence \sqrt n modulo 1
Duration: 1 hour 2 mins
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About this item
| Description: |
Vinogradov, I (University of Bristol)
Wednesday 18 June 2014, 14:30-15:30 |
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| Created: | 2014-07-10 09:45 |
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| Collection: | Interactions between Dynamics of Group Actions and Number Theory |
| Publisher: | Isaac Newton Institute |
| Copyright: | Vinogradov, I |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Let G=SL(2,\R)\ltimes R^2 and Gamma=SL(2,Z)\ltimes Z^2. Building on recent work of Strombergsson we prove a rate of equidistribution for the orbits of a certain 1-dimensional unipotent flow of Gamma\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 sqrt n mod 1. |
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