On continued fraction expansion of potential counterexamples to mixed Littlewood conjecture
1 hour 8 mins,
983.95 MB,
MPEG-4 Video
640x360,
29.97 fps,
44100 Hz,
1.92 Mbits/sec
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About this item
| Description: |
Badziahin, D (Durham University)
Tuesday 10 June 2014, 14:30-15:30 |
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| Created: | 2014-06-18 13:14 |
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| Collection: | Interactions between Dynamics of Group Actions and Number Theory |
| Publisher: | Isaac Newton Institute |
| Copyright: | Badziahin, D |
| 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: | Mixed Littlewood conjecture proposed by de Mathan and Teulie in 2004 states that for every real number x one has
lim infq→∞q⋅|q|D⋅||qx||=0. where |∗|D is a so called pseudo norm which generalises the standard p-adic norm. In the talk we'll consider the set \mad of potential counterexamples to this conjecture. Thanks to the results of Einsiedler and Kleinbock we already know that the Haudorff dimension of \mad is zero, so this set is very tiny. During the talk we'll see that the continued fraction expansion of every element in \mad should satisfy some quite restrictive conditions. As one of them we'll see that for these expansions, considered as infinite words, the complexity function can neither grow too fast nor too slow. |
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