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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

Sažetak

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.

Ključne riječi

Approximation by algebraic numbers; Schmidt Subspace Theorem

Hrčak ID:

44049

URI

https://hrcak.srce.hr/44049

Datum izdavanja:

9.12.2009.

Posjeta: 1.476 *