Mesures de transcendance et d'indépendance algébrique de fractions continues
DOI:
https://doi.org/10.22199/S07160917.1999.0002.00006Keywords:
Fraction continue, Mesure, Transcendance, Indépendance algébriqueAbstract
Dans cet article, on donne des conditions suffisantes sur les fractions continues A et B pour que les nombres réels A, B, A + B, A - B, AB et A/ B soient transcendants. La méthode utilisée permet aussi de calculer une mesure de transcendance ainsi qu 'une mesure d'indépendance algébrique des fractions continues transcendantes.
References
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3. G.H. HARDY and E.M. WRIGHT- An introduction to the Theory of Numbers, Oxford Univ. Press, (1985).
4. A. KACHA - Approximation algébrique de fractions continues, C.R. Acad. Sci. Paris, t 317, Série 1, pp. 17-20, (1993).
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6. G. NETTLER- Transcendental continued fractions, J. Number Theory, 13, pp. 456-462, (1981).
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8. A.B. SHIDLOVSKII - Transcendental numbers, Walter de Gruyter (1989).
2. P. BUNDSCHUH - Transcendental continued fractions, J. Number Theory, 18, pp. 91-98, (1984).
3. G.H. HARDY and E.M. WRIGHT- An introduction to the Theory of Numbers, Oxford Univ. Press, (1985).
4. A. KACHA - Approximation algébrique de fractions continues, C.R. Acad. Sci. Paris, t 317, Série 1, pp. 17-20, (1993).
5. A. KACHA - Transcendance et fractions continues, Séminaire de Théorie des Nombres 1990, Université de Caen.
6. G. NETTLER- Transcendental continued fractions, J. Number Theory, 13, pp. 456-462, (1981).
7. T. O KAN O- A note on the transcendental continued fractions; Tokyo J. Math Vol. 10, n1, pp. 152-156, (1987).
8. A.B. SHIDLOVSKII - Transcendental numbers, Walter de Gruyter (1989).
Published
2018-04-04
How to Cite
[1]
A. Kacha, “Mesures de transcendance et d’indépendance algébrique de fractions continues”, Proyecciones (Antofagasta, On line), vol. 18, no. 2, pp. 183-193, Apr. 2018.
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