skip to content
 

On the p-adic Littlewood conjecture for quadratics

Presented by: 
P Bengoechea University of York
Date: 
Friday 27th June 2014 - 14:30 to 15:30
Venue: 
INI Seminar Room 2
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 $inf_{q?1} q·||qx||·|q|_p = 0$ 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 $lim inf_{q?1} q·log(q)·||qx||·|q|_p$ 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.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons