Length of the sum and product of algebraic numbers

被引：2

作者：

Dubickas, A ^{[1
]}

Smyth, CJ

机构：

[1] Vilnius State Univ, Inst Math & Informat, Vilnius, Lithuania

[2] Univ Edinburgh, Dept Math & Stat, Edinburgh EH8 9YL, Midlothian, Scotland

来源：

MATHEMATICAL NOTES | 2005年 / 77卷 / 5-6期

关键词：

algebraic number; length function; height function; Mahler measure; Lehmer conjecture;

D O I：

10.1007/s11006-005-0079-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper, we consider products of lengths of algebraic numbers whose sum or product is a chosen algebraic number. These products are used to construct a new height function for algebraic numbers. With the help of this function, a metric on the set of all algebraic numbers, which induces the discrete topology, is introduced.

引用

页码：787 / 793

页数：7