A dynamical construction of small totally p-adic algebraic numbers

被引：3

作者：

Petsche, Clayton ^{[1
]}

Stacy, Emerald ^{[2
]}

机构：

[1] Oregon State Univ, Dept Math, Corvallis, OR 97331 USA

[2] Washington Coll, Dept Math & Comp Sci, 300 Washington Ave, Chestertown, MD 21620 USA

来源：

JOURNAL OF NUMBER THEORY | 2019年 / 202卷

关键词：

Weil height; Small points; Totally p-adic algebraic numbers; Arakelov-Zhang pairing; EQUIDISTRIBUTION; HEIGHTS; POINTS;

D O I：

10.1016/j.jnt.2019.01.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a dynamical construction of an infinite sequence of distinct totally p-adic algebraic numbers whose Weil heights tend to the limit log p/p-1, thus giving a new proof of a result of Bombieri-Zannier. The proof is essentially equivalent to the explicit calculation of the Arakelov-Zhang pairing of the maps sigma(x) = x(2) and phi(p)(x) = 1/p(x(p) - x). (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：27 / 36

页数：10

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