THE TRACE PROBLEM FOR TOTALLY POSITIVE ALGEBRAIC INTEGERS

被引：22

作者：

Liang, Yanhua ^{[1
]}

Wu, Qiang ^{[1
]}

机构：

[1] SW Univ China, Dept Math, Chongqing 400715, Peoples R China

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2011年 / 90卷 / 03期

关键词：

absolute trace; totally positive algebraic integer; Salem number; explicit auxiliary function; semi-infinite linear programming; LLL algorithm; SALEM-NUMBERS;

D O I：

10.1017/S1446788711001030

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let a be a totally positive algebraic integer of degree d >= 2 and alpha(1) = alpha, alpha(2), ... alpha(d), be all its conjugates. We use explicit auxiliary functions to improve the known lower bounds of S-k/d, where S-k = Sigma(d)(i=1) alpha(k)(i) and k = 1, 2, 3. These improvements have consequences for the search of Salem numbers with negative traces.

引用

页码：341 / 354

页数：14

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