Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T14:02:01.841Z Has data issue: false hasContentIssue false

Arithmetic properties of certain functions in several variables II

Published online by Cambridge University Press:  09 April 2009

J. H. Loxton
Affiliation:
School of Mathematics, University of New South Wales, Kensington NSW 2033, Australia.
A. J. van der Poorten
Affiliation:
School of Mathematics, University of New South Wales, Kensington NSW 2033, Australia.
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.

If T = (tij) is an n x n matrix with non-negative integer entries, we define a transformation T: CnCn by z' = Tz where

.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1977

References

Gantmacher, F. R. (1959), Applications of the theory of matrices, (Interscience, New York).Google Scholar
Kronecker, L. (1857), Zwei über Gleichungen mit ganzzahligen Coefficienten, J. reine angew. Math. 53, 173175.Google Scholar
Lang, S. (1966), Introduction to transcendental numbers, (Addison-Wesley, Reading, Massachusetts).Google 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, ed. Baker, A. and Masser, D. W. (Academic Press), Chapter 15, 211226.Google Scholar
Loxton, J. H. and van der Poorten, A. J. (1977), Arithmetic properties of certain functions in several variables, J. Number Theory 9, 87106.Google Scholar
Loxton, J. H. and van der Poorten, A. J. (to appear), A class of hypertranscendental functions, Aequationes Math.Google Scholar
Mahler, K. (1929), Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101, 342366.Google Scholar
Mahler, K. (1930), Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen, Math. Z. 32, 545585.Google Scholar
van der Waerden, B. L. (1971), How the proof of Baudet's conjecture was found, Studies in Pure Mathematics, ed. Mirsky, L. (Academic Press, London), 251260.Google Scholar