Diophantine Approximation and Continued Fraction Expansions of Algebraic Power Series in Positive Characteristic

AbstractIn a recent paper M. Buck and D. Robbins have given the continued fraction expansion of an algebraic power series when the base field is F3. We study its rational approximation property in relation with Roth's theorem, and we show that this element has an analog for each power of an odd prime number. At last we give the explicit continued fraction expansion of another classical example