Survey and Additional Properties on the Transcendence Order over Q(p) in C-p

被引：0

作者：

Escassut, A. ^{[1
]}

机构：

[1] Univ Blaise Pascal Cezeaux, UMR 6620, Lab Math, F-63171 Aubiere, France

来源：

P-ADIC NUMBERS ULTRAMETRIC ANALYSIS AND APPLICATIONS | 2015年 / 7卷 / 01期

关键词：

p-adic transcendence; transcendence order;

D O I：

10.1134/S2070046615010021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper is aimed at recalling the notion of transcendence order over Q(p) and its main properties. Proofs are more detailed than in the paper published in Journal of Number Theory. The main results: the order always is >= 1 and we construct a number b that is of order 1 + is an element of for every is an element of > 0. If a is of order <= t and if b is transcendental over Q(p) but algebraic over Q(p)(a), then b is of order <= t too. Finally, numbers of infinite order are constructed.

引用

页码：17 / 23

页数：7

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