Salem numbers and Pisot numbers via interlacing

Details Salem numbers and Pisot numbers via interlacing Salem numbers and Pisot numbers via interlacing

2010-08-04

arxiv.org/abs/1008.0731v2

Mathematics

Number Theory

21 pages, 5 figures, updated in response to reviewer comments

Scientific paper

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 show that all Salem numbers are produced via an interlacing construction.

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