On algebraic independence of some continued fractions

Author:

Kacha AliORCID,Ahallal Sarra

Abstract

In the present paper, we prove the algebraic independence of a finite number of real continued fractions which have partial quotients that increase rapidly. We then use a general Liouville criteria to justiy the algebraic independence of limits of some real series. We note that these results extend some work of Bundschuh and we use a new and simple method.

Publisher

Sociedade Paranaense de Matemática

Reference13 articles.

1. Adams, W. W., The algebraic independence of certain Liouville continued fractions, Proc. Amer. Math. Soc., 95(4), 521-516, (1985).

2. Belhroukia K. and Kacha, A., Transcendence and approximation measure of continued fraction, Int. J. Open Problems Compt. Math., 11(4), 1-14, (2018).

3. Bundschuh,P., Transcendental continued fractions, J. Number Theory 18, 91-98, (1984).

4. Durand, A., Indépendance algébrique de nombres complexes et critères de transcendance, compositio. Math. 35, 259-267, (1977).

5. Kacha, A., Approximation algébrique de fractions continues, C R. Acad. Sci. Paris, t. 317, Série I, 17-20, (1993).

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