Pisot and Salem numbers in intervals of the real line
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In this paper, the authors developed an algorithm for determining all the Pisot numbers in an interval of the real line, provided this number is finite, and applied 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 reAbstract:
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 re-read more
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Journal ArticleDOI
Speculations concerning the range of Mahler's measure
TL;DR: In this paper, the authors describe Smyth's lecture at the University of British Columbia and present a number of proofs which would not be otherwise accessible as Appendix A. The attentive reader will soon realize the appropriateness of the title.
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Coxeter Groups, Salem Numbers and the Hilbert Metric
Journal ArticleDOI
On groups generated by two positive multi-twists: Teichmuller curves and Lehmer's number
TL;DR: In this article, the authors derive several interesting facts about subgroups of the mapping class group generated by two positive multi-twists, and identify all configurations of curves for which the corresponding groups fail to be free.
Book ChapterDOI
Number Theory and Polynomials: The Mahler measure of algebraic numbers: a survey
TL;DR: A survey of results for Mahler measure of algebraic numbers, and one-variable polynomials with integer coefficients is presented in this article, where the maximum modulus of the conjugates of an algebraic integer are also discussed.
Book ChapterDOI
The Mahler measure of algebraic numbers: a survey
TL;DR: A survey of results for Mahler measure of algebraic numbers, and one-variable polynomials with integer coefficients is presented in this article, where the maximum modulus of the conjugates of an algebraic integer are also discussed.
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The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
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