Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-21T06:36:45.509Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalised simultaneous approximation of functions

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  09 April 2009

A. J. Van Der Poorten
A. J. Van Der Poorten
Affiliation:
School of Mathematics, Physics, Computing and ElectronicsMacquarie UniversityNSW 2109Australia
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 generalise the approximation theory described in Mahier's paper “Perfect Systems” to linked simultaneous approximations and prove the existence of nonsingular approximation and of transfer matrices by generalising Coates' normality zig-zag theorem. The theory sketched here may have application to constructions important in the theory of diophantine approximation.

MSC classification

Secondary: 11J61: Approximation in non-Archimedean valuations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 1 , August 1991 , pp. 50 - 61
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Coates, John, ‘On the algebraic approximation of functions I, II, III’, Nederl. Akad Wetensch. Proc. Ser. A 69 (1966), 421–461; IV, Nederl. Akad Wetensch. Proc. Ser. A 70 (1967), 205–212.CrossRefGoogle Scholar
[2]Hermite, C., ‘Sur la fonction exponentielle’, Oeuvres 3 (1873), 151–181.Google Scholar
[3]Hermite, C., ‘Sur la généralisation des fractions continues algébriques’, Oeuvres 4 (1893), 357–377.Google Scholar
[4]Jager, H., ‘A multidimensional generalization of the Padé table’, Nederl Akad. Wetensch. Proc. Ser. A 67 (1964), 192–249.Google Scholar
[5]Loxton, J. H. and van der Poorten, A. J., ‘Multidimensional generalisations of the Padé table’, Rocky Mountain J. Math. 9 (1979), 385–393.CrossRefGoogle Scholar
[6]Loxton, J. H. and van der Poorten, A. J., ‘Arithmetic properties of automata: regular sequences’, J. für Math. 330 (1988), 159–172.Google Scholar
[7]Mahler, Kurt, ‘Perfect systems’, Compositio Math. 9 (1968), 95–166.Google Scholar