Salem Numbers and Pisot Numbers via Interlacing

McKee, James ; Smyth, Chris

Canadian journal of mathematics, Tome 64 (2012) no. 2, pp. 345-367

Résumé

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.

Détail

DOI : 10.4153/CJM-2011-051-2

Mots-clés : 11R06, Salem numbers, Pisot numbers

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