On the fractional parts of powers of Pisot numbers of length at most 4

被引：2

作者：

Dubickas, Arturas ^{[1
]}

Jankauskas, Jonas ^{[2
]}

机构：

[1] Vilnius State Univ, Dept Math & Informat, LT-03225 Vilnius, Lithuania

[2] Univ Waterloo, Dept Pure Math, 200 Univ Ave West, Waterloo, ON N2L 3G1, Canada

来源：

JOURNAL OF NUMBER THEORY | 2014年 / 144卷

关键词：

Pisot numbers; Fractional parts; NEIGHBORHOOD;

D O I：

10.1016/j.jnt.2014.05.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is twofold. We first give a list of all Pisot polynomials of length at most 4. It contains seven polynomials of degree at most 5, and two infinite series of polynomials with unbounded degree. Then, for Pisot numbers alpha of length 3 and 4, we find explicitly the largest positive number L(alpha) such that for some xi = xi(alpha) is an element of R the limit points of the sequence of fractional parts {xi alpha(n)}(n=1)(infinity) all lie in the interval [L(alpha), 1 - L(alpha)]. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：325 / 339

页数：15

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