On Complex Pisot Numbers That Are Roots of Borwein Trinomials

被引:0
|
作者
Drungilas, Paulius [1 ]
Jankauskas, Jonas [1 ]
Junevicius, Grintas [1 ]
机构
[1] Vilnius Univ, Inst Math, Dept Math & Informat, Naugarduko 24, LT-03225 Vilnius, Lithuania
关键词
Borwein trinomial; complex Pisot number; unimodular number; root of unity; MAHLER MEASURES; SALEM-NUMBERS; POWERS; SEQUENCES;
D O I
10.3390/math12081129
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let n> m be positive integers. Polynomials of the form z(n )+/- z(m )+/- 1 are called Borwein trinomials. Using an old result of Bohl, we derive explicit formulas for the number of roots of a Borwein trinomial inside the unit circle |z|<1. Based on this, we determine all Borwein trinomials that have a complex Pisot number as a root. There are exactly 29 such trinomials.
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页数:10
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