EFFECTIVE RESULTS FOR RESTRICTED RATIONAL APPROXIMATION TO QUADRATIC IRRATIONALS

@article{Bennett2012EFFECTIVERF,
title={EFFECTIVE RESULTS FOR RESTRICTED RATIONAL APPROXIMATION TO QUADRATIC IRRATIONALS},
author={Michael A. Bennett and Yann Bugeaud},
journal={Acta Arithmetica},
year={2012},
volume={155},
pages={259-269}
}
• Published 2012
• Mathematics
• Acta Arithmetica
In this paper, we deduce a number of eective lower bounds upon the distance to an integer of quantities of the shape b n , where b and n are integers and is a real quadratic irrational. For certain , we obtain inequalities that approach in strength the corresponding ineective results arising from the p-adic version of Roth's theorem.
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We prove a general effective result concerning approximation of irrational values at rational points a / b of any G-function F with rational Taylor coefficients by fractions of the form n/(B\cdot

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