University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > On continued fraction expansion of potential counterexamples to mixed Littlewood conjecture.

On continued fraction expansion of potential counterexamples to mixed Littlewood conjecture.

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Mustapha Amrani.

Interactions between Dynamics of Group Actions and Number Theory

Mixed Littlewood conjecture proposed by de Mathan and Teulie in 2004 states that for every real number $x$ one has $$ liminf_{q oinfty} qot |q|_Dot ||qx|| = 0. $$ 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2019 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity