Effective Ratner equidistribution for SL(2,R)⋉(R2)⊕k and applications to quadratic forms
Duration: 58 mins 36 secs
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About this item
| Description: |
Strombergsson, A (Uppsala Universitet)
Thursday 26 June 2014, 13:30-14:30 |
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| Created: | 2014-07-11 14:16 |
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| Collection: | Interactions between Dynamics of Group Actions and Number Theory |
| Publisher: | Isaac Newton Institute |
| Copyright: | Strombergsson, A |
| 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)⋉(R2)⊕k and let Γ be a congruence subgroup of SL(2,Z)⋉(Z2)⊕k. I will present a result giving effective equidistribution of 1-dimensional unipotent orbits in the homogeneous space Γ∖G. The proof involves spectral analysis and use of Weil's bound on Kloosterman sums. I will also discuss applications to effective results for variants of the Oppenheim conjecture on the density of Q(Zn) on the real line, where Q is an irrational indefinite quadratic form. (Based on joint work with Pankaj Vishe.) |
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