Masaaki Amou

Approximation to certain transcendental decimal fractions by algebraic numbers

In this paper, we treat certain decimal fractions defined by Mahler and study approximations to these numbers by algebraic numbers of bounded degree. For this purpose, we give an estimate for the values of Mahlers function wd and of Koksmas function wd*. As an application of our estimate, we can show, for example, that the irrationality measure of the decimal fraction 0.123456789101112… is 10.

Arithmetical Properties of Solutions of Linear Second Order q-Difference Equations

A linear independence measure is obtained for the values F(t) and F(qt) of solutions F(z) of linear second order q-difference equations. From the result an irrationality measure for certain continued fractions is derived.