On the p-adic Littlewood conjecture for quadratics
51 mins 55 secs,
746.57 MB,
MPEG-4 Video
640x360,
29.97 fps,
44100 Hz,
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About this item
| Description: |
Bengoechea, P (University of York)
Friday 27 June 2014, 14:30-15:30 |
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| Created: | 2014-07-11 15:12 |
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| Collection: | Interactions between Dynamics of Group Actions and Number Theory |
| Publisher: | Isaac Newton Institute |
| Copyright: | Bengoechea, P |
| 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 ||·|| denote the distance to the nearest integer and, for a prime number p, let |·|_p denote the p-adic absolute value. In 2004, de Mathan and Teulié asked whether infq?1q⋅||qx||⋅|q|p=0 holds for every badly approximable real number x and every prime number p. When x is quadratic, the equality holds and moreover, de Mathan and Teullié proved that liminfq?1q⋅log(q)⋅||qx||⋅|q|p is finite and asked whether this limit is positive. We give a new proof of de Mathan and Teullié's result by exploring the continued fraction expansion of the multiplication of x by p with the help of a recent work of Aka and Shapira. We will also discuss the positivity of the limit. |
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