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Summary: Constructions of Pisot and Salem numbers
with flat palindromes
Shigeki Akiyama
and DoYong Kwon
Abstract
This paper introduces explicit conditions for some natural family
of polynomials to define Pisot or Salem numbers, and reviews related
topics as well as their references.
2000 Mathematics Subject Classification: 11R06, 30C15.
Keywords: Pisot number, Salem number.
1 Introduction
A Pisot (resp. Salem) number is an algebraic integer > 1 whose Galois
conjugates other than have moduli less than 1. (resp. less than or equal to
1 and at least one conjugate lies on the unit circle.) These algebraic numbers
unexpectedly or exceptionally appeared in number of quite different branches
of mathematics. A comprehensive survey is found in the book [11]. However,
related areas are still steadily expanding. To give convenient pointers to the
reader, we only mention some of such areas with surveys/recent papers :
· Number theory (Uniform distribution [24], -expansion [8, 1], Lehmer's
problem [12, 45]),
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