Salem numbers, Pisot numbers, Mahler measure and graphs

Details Salem numbers, Pisot numbers, Mahler measure and graphs Salem numbers, Pisot numbers, Mahler measure and graphs

2005-03-23

arxiv.org/abs/math/0503480v1

Mathematics

Number Theory

28 pages, 7 figures

Scientific paper

We use graphs to define sets of Salem and Pisot numbers, and prove that the union of these sets is closed, supporting a conjecture of Boyd that the set of all Salem and Pisot numbers is closed. We find all trees that define Salem numbers. We show that for all integers n the smallest known element of the n-th derived set of the set of Pisot numbers comes from a graph. We define the Mahler measure of a graph, and find all graphs of Mahler measure less than (1+sqrt5)/2. Finally, we list all small Salem numbers known to be definable using a graph.

Affiliated with

Also associated with

No associations

Rating

Salem numbers, Pisot numbers, Mahler measure and graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Salem numbers, Pisot numbers, Mahler measure and graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Salem numbers, Pisot numbers, Mahler measure and graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-135075