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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Arithmetic Study Group: On recent developments related to p-adic Littlewood conjecture (Part II)

Presented by Dmitry Badziahin, Durham University

19 November 2013 16:00 in ES 236

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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