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Transcendence measures by Mahler's transcendence method

Published online by Cambridge University Press:  17 April 2009

Paul-Georg Becker-Landeck
Paul-Georg Becker-Landeck
Affiliation:
Remigiusstrasse 37, D-5000 KöLN 41, West Germany.
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Abstract

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Let f(z) be an analytic function in the unit circle satisfying the functional equation f(z) = a(z) f(zρ) + b(z), where ρ is a natural number and a(z), b(z) are polynomials. If α is an algebraic number, we give a transcendence measure for f(α). This improves earlier results of Galochkin and Miller.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 1 , February 1986 , pp. 59 - 65
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Becker-Landeck, P. -G., Quantitative Resultate im Zusammenhang mit der Mahlerschen Transzendenzmethode (Dissertation, Universität zu Köln, 1984).Google Scholar
[2]Becker-Landeck, P. -G., “Maße für algebraische Unabhängigkeit”, (to appear).Google Scholar
[3]Galochkin, A.I., “Transcendence measure of values of functions satisfying certain functional equation”, Math. Notes 27 (1980), 83–88.CrossRefGoogle Scholar
[4]Lang, S., Introduction to transcendental numbers, (Addison-Wesley, Reading, 1966).Google Scholar
[5]Mahler, K., “Arithmetische Eigenschaften der Lösungan einer Klasse von Funktionalgleichungen”, Math. Ann. 101 (1929), 342–366.CrossRefGoogle Scholar
[6]Miller, W., “Transcendence measures by a method of Mahler”, J. Austral. Math. Soc. Ser. A 32 (1982), 68–78.CrossRefGoogle Scholar
[7]Schneider, T., Einfuhrung in die transzendanten Zahlen (Springer, Berlin, 1957).CrossRefGoogle Scholar
[8]Waldschmidt, M., Nombres transcendants, (Lecture notes in mathematics 402, Springer, Berlin, 1974).CrossRefGoogle Scholar