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On a Transcendence Problem of K. Mahler

Published online by Cambridge University Press:  20 November 2018

K. K. Kubota*
Affiliation:
Institut des Hautes Etudes Scientifiques Bur es-sur-Yvette, France; University of Kentucky, Lexington, Kentucky
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Abstract

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K. Mahler [8] has proposed the following problem. Let Ωr for r ≧ 1 be a sequence of n X n non-negative rational integer matrices. Each Ωrrij) defines a map Ωr : Cn⟶ Cn by

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Kubota, K. K., On the algebraic independence of holomorphic solutions of certain functional equations and their values, to appear, Math. Ann.Google Scholar
2. Kubota, K. K. On Mahler's algebraic independence method, to appear.Google Scholar
3. Lang, S., Introduction to transcendental numbers (Addison-Wesley, Reading, Mass., 1966).Google Scholar
4. Loxton, J. H. and A. J. van der Poorten, Arithmetic properties of certain functions in several variables I, II, III, to appear.Google Scholar
5. Transcendence and algebraic independence by a method of Mahler, to appear in Advances in Transcendence Theory.Google Scholar
6. Mahler, K., Arithmetische Eigenschaften der Lbsun gen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342366.Google Scholar
7. Mahler, K. Tiber das Verschwinden von Potenzreihen mehrerer Verdnderlichen im speziellen Punktfolgen, Math. Ann. 103 (1930), 573587.Google Scholar
8. Mahler, K. Remarks on a paper of W. Schwarz, J. Number Theory 1 (1969), 512521.Google Scholar
9. Nagata, M., Local rings (Interscience, N.Y., N.Y., 1962).Google Scholar