Algebraic Numbers and Algebraic Integers

ثبت نشده
چکیده

c © W W L Chen, 1984, 2013. This chapter originates from material used by the author at Imperial College London between 1981 and 1990. It is available free to all individuals, on the understanding that it is not to be used for financial gain, and may be downloaded and/or photocopied, with or without permission from the author. However, this document may not be kept on any information storage and retrieval system without permission from the author, unless such system is not accessible to any individuals other than its owners.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Approximation of complex algebraic numbers by algebraic numbers of bounded degree

To measure how well a given complex number ξ can be approximated by algebraic numbers of degree at most n one may use the quantities w n (ξ) and w * n (ξ) introduced by Mahler and Koksma, respectively. The values of w n (ξ) and w * n (ξ) have been computed for real algebraic numbers ξ, but up to now not for complex, non-real algebraic numbers ξ. In this paper we compute w n (ξ), w * n (ξ) for a...

متن کامل

Counting Perron Numbers by Absolute Value

We count various classes of algebraic integers of fixed degree by their largest absolute value. The classes of integers considered include all algebraic integers, Perron numbers, totally real integers, and totally complex integers. We give qualitative and quantitative results concerning the distribution of Perron numbers, answering in part a question of W. Thurston [Thu].

متن کامل

ALGEBRAIC INDEPENENCE OF CERTAIN FORMAL POWER SERIES (II)

We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)

متن کامل

PartII Number Fields

1 Algebraic number fields 3 1.1 Algebraic numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Algebraic number fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Norm and Trace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Algebraic integers . . . . . . . . . . . . . . . . . . . . . . . . ....

متن کامل

On algebraic integers in short intervals and near smooth curves

In 1970 A. Baker and W. Schmidt introduced the concept of a regular system of numbers and vectors. They proved that the set of real algebraic numbers forms a regular system on any fixed interval. This fact has allowed to prove some important results in the metric theory of transcendental numbers. In this paper their approach is applied to the set of algebraic integers α in short intervals of le...

متن کامل

Math 784: algebraic NUMBER THEORY

Algebraic Number Theory: • What is it? The goals of the subject include: (i) to use algebraic concepts to deduce information about integers and other rational numbers and (ii) to investigate generalizations of the integers and rational numbers and develop theorems of a more general nature. Although (ii) is certainly of interest, our main point of view for this course will be (i). The focus of t...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013