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.
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页码：27 / 36
页数：10
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