Explicit Lower Bounds for Rational Approximation to Algebraic Numbers

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 speciic bounds of the avour of 3 p 2 ? p q > 1 4 q ?2:45 and 7 p 5 ? p q > 1 4 q ?4:43 which we show to hold for any nonzero integers p and q. Further examples are tabulated and applications to Diophantine equations are brieey discussed as are other topics of related interest.