Salem numbers and Pisot numbers via interlacing

James McKee, Christopher Smyth

Research output: Contribution to journalArticlepeer-review


We present a general construction of Salem numbers via rational functions whose zeros and poles mostly lie on the unit circle and satisfy an interlacing condition. This extends and unifies earlier work. We then consider the ``obvious'' limit points of the set of Salem numbers produced by our theorems and show that these are all Pisot numbers, in support of a conjecture of Boyd. We then show that all Pisot numbers arise in this way. Combining this with a theorem of Boyd, we produce all Salem numbers via an interlacing construction.
Original languageEnglish
Pages (from-to)345-367
Number of pages23
JournalCanadian Journal of Mathematics
Issue number2
Early online date3 Aug 2011
Publication statusPublished - Apr 2012


  • Salem numbers
  • Pisot numbers


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