Integer Relations Among Algebraic Numbers
نویسندگان
چکیده
منابع مشابه
Integer Relations Among Algebraic Numbers
A vector m = (mx , ... , mn) eZ"\ {0} is called an integer relation for the real numbers a,, ... , an , if X)0,"1, = 0 holds. We present an algorithm that, when given algebraic numbers ax , ... , an and a parametere , either finds an integer relation for a,,... , an or proves that no relation of Euclidean length shorter than 1/e exists. Each algebraic number is assumed to be given by its minima...
متن کاملQuadratic relations between logarithms of algebraic numbers
A well known conjecture asserts that Q-linearly independent logarithms of algebraic numbers should be algebraically independent. So far it has only been proved that they are linearly independent over the field of algebraic numbers (Baker, 1966). It is not yet known that there exist two logarithms of algebraic numbers which are algebraically independent. The next step might be to consider quadra...
متن کاملOn the Hardness of Approximating Shortest Integer Relations among Rational Numbers
Given x 2 R n an integer relation for x is a non-trivial vector m 2 Z n with inner product hm; xi = 0. In this paper we prove the following: Unless every NP language is recognizable in deterministic quasi-polynomial time, i.e., in time O(n poly(log n)), thè 1-shortest integer relation for a given vector x 2 Q n cannot be approximated in polynomial time within a factor of 2 log 0:5? n , where is...
متن کاملAlgebraic 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 کاملHomoroot Integer Numbers
In this paper we first define homorooty between two integer numbers and study some of their properties. Thereafter we state some applications of the homorooty in studying and solving some Diophantine equations and systems, as an interesting and useful elementary method. Also by the homorooty, we state and prove the necessary and sufficient conditions for existence of finite solutions in a speci...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1990
ISSN: 0025-5718
DOI: 10.2307/2008706