Number Theory Seminar

Liam Orovec, University of Waterloo

Greedy and Lazy Parry Numbers

We say a real number \beta is a Parry number provided the greedy \beta-expansion for 1 is eventually periodic or finite. We show conditions for when \beta is a Parry number and provide a family of real numbers which are always Parry numbers, the PV-numbers. The related Salem numbers, constructed from PV-numbers are then considered. We split this into four cases, the first of which was shown by Hare and Tweedle, we give criteria for finding Salem numbers which are Parry numbers. Time permitting we will explore the case where we look at lazy expansions instead of greedy expansions, we call these numbers lazy Parry numbers.

MC 5417