Hostname: page-component-6d856f89d9-sp8b6 Total loading time: 0 Render date: 2024-07-16T04:13:29.578Z Has data issue: false hasContentIssue false
  • English
  • Français

Transcendence measures by a method of Mahler

Published online by Cambridge University Press:  09 April 2009

William Miller
William Miller
Affiliation:
School of Natural Resources, The University of The South Pacific, Box 1168, Suva, Fiji
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.

Suppose that f(z) is a function of one complex variable satisfying

where ρ is an integer larger than 1 and a(z) and b(z) are rational functions. We consider f evaluated at the algebraic point a and develop a transcendence measure for f(α) under suitable conditions on f and α.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 1 , January 1982 , pp. 68 - 78
Copyright
Copyright © Australian Mathematical Society 1982

References

Lang, S. (1965), Algebra (Addison-Wesley, Reading, Massachusetts).Google Scholar
Lang, S. (1966), Introduction to transcendental numbers (Addison-Wesley, Reading, Massachusetts).Google Scholar
Loxton, J. H. and van der Poorten, A. J. (1976), ‘On algebraic functions satisfying a class of functional equations’, Aequations Math. 14, 413–420.CrossRefGoogle Scholar
Loxton, J. H. and van der Poorten, A. J. (1977), ‘Transcendence and algebraic independence by a method of Mahler’, Transcendence Theory-Advances and Applications, edited by Baker, A. and Masser, D. W., Chapter 15, pp. 211–226 (Academic Press).Google Scholar
Kubota, K. K. (1977), ‘On the algebraic independence of holomorphic solutions of certain functional equations and their values’, Math. Ann. 227, 9–50.CrossRefGoogle Scholar
Mahler, K. (1929), ‘Arithmetische Eigenschaften der Losungen einer Klasse von Funktionalgleichungen’, Math. Ann. 101 342–366.CrossRefGoogle Scholar
Miller, W. (1979), Transcendence measures for values of analytic solutions to certain functional equations (Ph.D. Thesis, University of Michigan).Google Scholar
Waldschmidt, M. (1974), Nombres transcendants, Lecture Notes in Mathematics, 402 (Springer, Berlin).CrossRefGoogle Scholar