Algebraic Numbers
نویسندگان
چکیده
منابع مشابه
Algebraic Numbers and Algebraic Integers
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 an...
متن کاملOn the Approximation to Algebraic Numbers by Algebraic Numbers
Let n be a positive integer. Let ξ be an algebraic real number of degree greater than n. It follows from a deep result of W. M. Schmidt that, for every positive real number ε, there are infinitely many algebraic numbers α of degree at most n such that |ξ−α| < H(α)−n−1+ε, where H(α) denotes the näıve height of α. We sharpen this result by replacing ε by a function H 7→ ε(H) that tends to zero wh...
متن کاملExpansions of algebraic numbers
Classical ways to represent a real number are by its continued fraction expansion or by its expansion in some integer base. It is commonly expected that algebraic irrational numbers behave, in many respects, like almost all numbers. For instance, their decimal expansion should contain every finite block of digits from {0, . . . , 9}. We are very far away from establishing such a strong assertio...
متن کاملSemi-algebraic Ramsey Numbers
Given a finite point set P ⊂ R, a k-ary semi-algebraic relation E on P is the set of k-tuples of points in P , which is determined by a finite number of polynomial equations and inequalities in kd real variables. The description complexity of such a relation is at most t if the number of polynomials and their degrees are all bounded by t. The Ramsey number R k (s, n) is the minimum N such that ...
متن کاملNotes on Algebraic Numbers
This is a summary of my 1994–1995 course on Algebraic Numbers. (Revised and improved on 1993– 1994!) The background assumed is standard elementary number theory—as found in my Level III course—and a little (Abelian) group theory. Corrections and suggestions for improvement are welcome, and will be credited in future editions! I first learned algebraic number theory from Stewart & Tall’s book ([...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2016
ISSN: 1898-9934,1426-2630
DOI: 10.1515/forma-2016-0025