Skip to main content
Article thumbnail
Location of Repository

By Artūras Dubickas and Chris Smyth


We show that the number of distinct non-parallel lines passing through two conjugates of an algebraic number α of degree d ≥ 3 is at most [d 2 /2] − d + 2, its conjugates being in general position if this number is attained. If, for instance, d ≥ 4 is even, then the conjugates of α ∈ Q of degree d are in general position if and only if α has 2 real conjugates, d − 2 complex conjugates, no three distinct conjugates of α lie on a line, and any two lines that pass through two distinct conjugates of α are non-parallel, except for d/2 − 1 lines parallel to the imaginary axis. Our main result asserts that the conjugates of any Salem number are in general position. We also ask two natural questions about conjugates of Pisot numbers which lead to the equation α1 + α2 = α3 + α4 in distinct conjugates of a Pisot number. The Pisot number α1 = (1+ √ 3 + 2 √ 5)/2 shows that this equation has such a solution. 1

Year: 2013
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.