Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T00:05:58.947Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Transcendence Problem of K. Mahler

Published online by Cambridge University Press:  20 November 2018

K. K. Kubota
K. K. Kubota*
Affiliation:
Institut des Hautes Etudes Scientifiques Bur es-sur-Yvette, France; University of Kentucky, Lexington, Kentucky
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 Ωr — (ωrij) defines a map Ωr : Cn —⟶ Cn by

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 3 , 01 June 1977 , pp. 638 - 647
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), 342–366.Google Scholar
7. Mahler, K. Tiber das Verschwinden von Potenzreihen mehrerer Verdnderlichen im speziellen Punktfolgen, Math. Ann. 103 (1930), 573–587.Google Scholar
8. Mahler, K. Remarks on a paper of W. Schwarz, J. Number Theory 1 (1969), 512–521.Google Scholar
9. Nagata, M., Local rings (Interscience, N.Y., N.Y., 1962).Google Scholar