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arXiv · 0712.2304

On simultaneous rational approximations to a real number, its square, and its cube

Damien Roy
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Abstract

We provide an upper bound on the uniform exponent of approximation to a triple (xi, xi^2, xi^3) by rational numbers with the same denominator, valid for any transcendental real number xi. This upper bound refines a previous result of Davenport and Schmidt. As a consequence, we get a sharper lower bound on the exponent of approximation of such a number xi by algebraic integers of degree at most 4.

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Damien Roy. 2007-12-15. On simultaneous rational approximations to a real number, its square, and its cube. https://doi.org/10.4064/aa133-2-6

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