Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-16T13:09:13.553Z Has data issue: false hasContentIssue false
  • English
  • Français

Algebraic independence by a method of Mahler

Part of: Difference equations Difference and functional equations

Published online by Cambridge University Press:  09 April 2009

Yuval Z. Flicker
Yuval Z. Flicker
Affiliation:
Institute for Advanced Study Princeton, New Jersey 08540, U.S.A.
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.

We establish a general algebraic independence theorem for the solutions of a certain kind of functional equations. As a particular application, we prove that for any real irrational ζ, the numbers are algebraically independent, for multiplicatively independent algebraic αi with 0<|<| <1.

MSC classification

Secondary: 39A30: Stability theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 2 , March 1979 , pp. 173 - 188
Copyright
Copyright © Australian Mathematical Society 1979

References

Kubota, K. K. (1977a), ‘On Mahler's algebraic independence method’, preprint.Google Scholar
Kubota, K. K. (1977b), ‘Linear functional equations and algebraic independence’, in Transcendence theory: advances and applications, edited by Baker, A. and Masser, D. W. (Academic Press).Google Scholar
Loxton, J. H. and van der Poorten, A. J. (1977), ‘Arithmetic properties of certain functions in several variables II’, J. Austral. Math. Soc. 24, 393–408.CrossRefGoogle Scholar
Loxton, J. H. and van der Poorten, A. J. (1977a), ‘Arithmetic properties of certain functions in several variables III’, Bull. Austral. Math. Soc. 16, 15–47.CrossRefGoogle Scholar
Loxton, J. H. and van der Poorten, A. J. (1977b), ‘Transcendence and algebraic independence by a method of Mahler’, in Transcendence theory: advances and applications, edited by Baker, A. and Masser, D. W. (Academic Press).Google Scholar
Mahler, K., (1969), ‘Remarks on a paper by W. Schwarz’, J. Number Theory 1, 512–521.CrossRefGoogle Scholar