Salem Numbers and Pisot Numbers via Interlacing
نویسندگان
چکیده
منابع مشابه
Salem Numbers, Pisot Numbers, Mahler Measure, and Graphs
We use graphs to define sets of Salem and Pisot numbers, and prove that the union of these sets is closed, supporting a conjecture of Boyd that the set of all Salem and Pisot numbers is closed. We find all trees that define Salem numbers. We show that for all integers n the smallest known element of the n-th derived set of the set of Pisot numbers comes from a graph. We define the Mahler measur...
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A Newman polynomial has all its coefficients in {0, 1} and constant term 1. It is known that every root of a Newman polynomial lies in the slit annulus {z ∈ C : τ−1 < |z| < τ} \ R+, where τ denotes the golden ratio, but not every polynomial having all of its conjugates in this set divides a Newman polynomial. We show that every negative Pisot number in (−τ,−1) with no positive conjugates, and e...
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Properties of Pisot numbers have long been of interest. One line of questioning, initiated by Erdős, Joó and Komornik in 1990, is the determination of l(q) for Pisot numbers q, where l(q) = inf(|y| : y = 0 + 1q + · · ·+ nq, i ∈ {±1, 0}, y 6= 0). Although the quantity l(q) is known for some Pisot numbers q, there has been no general method for computing l(q). This paper gives such an algorithm. ...
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Based on the work of Dufresnoy and Pisot, we develop an algorithm for determining all the Pisot numbers in an interval of the real line, provided this number is finite. We apply the algorithm to the problem of determining small Salem numbers by Salem's construction, and to the proof that certain Pisot sequences satisfy no linear recurrence relation. Introduction. A real algebraic integer 0 > 1 ...
متن کاملNumbers , Pisot Numbers , Mahler Measure and Graphs
We use graphs to define sets of Salem and Pisot numbers, and prove that the union of these sets is closed, supporting a conjecture of Boyd that the set of all Salem and Pisot numbers is closed. We find all trees that define Salem numbers. We show that for all integers n the smallest known element of the n-th derived set of the set of Pisot numbers comes from a graph. We define the Mahler measur...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2012
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2011-051-2