Student Number Theory seminar

Monday, May 13, 2013 11:30 am - 11:30 am EDT (GMT -04:00)

Blake Madill, Pure Mathematics, University of Waterloo

"Small Salem Numbers"

A great deal is known about the Pisot-Vijayaraghavan (P.V.) numbers. However, less is known about the set of Salem numbers. The main
result in this area, due to Salem, is that each P.V. number is a limit
point of the set of Salem numbers. The smallest known P.V. number is
approximately $\theta_0=1.3247$. Any interval $(0,a)$, $a\geq\theta_0,$ contains infinitely many Salem numbers. Therefore it is reasonable to be interested in small Salem numbers.

We present all relevant definitions and discuss results by Boyd, which
allow one to find Salem numbers from given P.V. numbers.