Arithmetic Study Group: On recent developments related to p-adic Littlewood conjecture
12 November 2013 17:00 in CM 103
The p-adic Littlewood conjecture was firstly posed by de Mathan and Teulie in 2004 and it is often considered as a "simplified version" of a famous Littlewood conjecture. In the series of two talks we'll consider the set "mad" of the counterexamples to this conjecture (which is believed to be empty). 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. In 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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