Explicit Lower Bounds for Rational Approximation to Algebraic Numbers
Michael A. Bennett · Proceedings of the London Mathematical Society · 1997
In this paper, we apply Pad'e approximation methods to derive completely explicit measures of irrationality for certain classes of algebraic numbers. Our approach is similar to that taken previously by G.V. Chudnovsky but has some fundamental advantages with regards to determining implicit constants. Our general results may be applied to produce specific bounds of the flavour of fi fi fi fi 3 p 2 \\Gamma p q fi fi fi fi ? 1 4 q \\Gamma2:45 and fi fi fi fi 7 p 5 \\Gamma p q fi fi fi fi ? 1 4 q \\Gamma4:43 which we show to hold for any nonzero integers p and q. Further examples are tabulated and applications to Diophantine equations are briefly discussed as are other topics of related interest. 1