Salem numbers, Pisot numbers, Mahler measure and graphs
| dc.creator | McKee, James | |
| dc.creator | Smyth, Chris | |
| dc.date | 2005-03-23 | |
| dc.date.accessioned | 2026-07-07T05:18:15Z | |
| dc.date.available | 2026-07-07T05:18:15Z | |
| dc.description | 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. | |
| dc.description | 28 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/math/0503480 | |
| dc.identifier | http://arxiv.org/abs/math/0503480 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74598 | |
| dc.subject | Number Theory | |
| dc.subject | 11R06;05C50 | |
| dc.title | Salem numbers, Pisot numbers, Mahler measure and graphs | |
| dc.type | text |