Salem numbers of negative trace

We prove that, for all d 4, there are Salem numbers of degree 2d and trace -1, and that the number of such Salem numbers is d/ (log log d)2 . As a consequence, it follows that the number of totally positive algebraic integers of degree d and trace 2d - 1 is also d/ (log log d)2 .

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: C. J. Smyth
• Keywords: MOC 2000, Salem Numbers, Totally Positive