http://dx.doi.org/10.4153/CJM-2011-051-2
Canad. J. Math. 64(2012), 345-367
Published:2011-08-03
Printed: Apr 2012
James McKee, Department of Mathematics, Royal Holloway, University of London, Egham Hill, Egham, Surrey TW20 0EX, UK Chris Smyth, School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3JZ, Scotland, UK
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Abstract
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.
© Canadian Mathematical Society, 2013
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