Glasnik matematički, Vol. 44 No. 2, 2009.
Original scientific paper
https://doi.org/10.3336/gm.44.2.05
On the approximation to algebraic numbers by algebraic numbers
Yann Bugeaud
; Université de Strasbourg, U. F. R. de mathématiques, 7, rue René Descartes, 67084 Strasbourg Cedex, France
Abstract
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 naive height of α. We sharpen this result by replacing ε by a function H ε(H) that tends to zero when H tends to infinity. We make a similar improvement for the approximation to algebraic numbers by algebraic integers, as well as for an inhomogeneous approximation problem.
Keywords
Approximation by algebraic numbers; Schmidt Subspace Theorem
Hrčak ID:
44049
URI
Publication date:
9.12.2009.
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