On algebraic approximations of certain algebraic numbers
نویسندگان
چکیده
منابع مشابه
Effective Irrationality Measures for Certain Algebraic Numbers
A result of Chudnovsky concerning rational approximation to certain algebraic numbers is reworked to provide a quantitative result in which all constants are explicitly given. More particularly, Padé approximants to the function (1 jc)1/3 are employed to show, for certain integers a and b, that |(a/fc) p/q\> cq~* when q > 0. Here, c and k are given as functions of a and b only. In 1964 Baker [1...
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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...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2003
ISSN: 0022-314X
DOI: 10.1016/s0022-314x(03)00068-4