Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-05T03:29:38.624Z Has data issue: false hasContentIssue false
  • English
  • Français

Remarks on generalised power sums

Published online by Cambridge University Press:  17 April 2009

Robert S. Rumely  and
A.J. van der Poorten
Robert S. Rumely
Affiliation:
Department of Mathematics, The University of Georgia, Athens, Georgia 30602, United States of America.
A.J. van der Poorten
Affiliation:
School of Mathematics, Physics, Computing and Electronics, Macquarie University, New South Wales 2113Australia.
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 give a description of factorisation in the ring of generalised power sums (the sequence of Taylor coefficients of rational functions regular at infinity) with a view to giving detailed bounds on the order of generalised power sum factors and roots of such sums.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 2 , October 1987 , pp. 311 - 329
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Bézivin, J.-P., “Factorisation de suites récurrentes linéaires et applications”, Bull. Soc. Math. France 112 (1984), 365–376.CrossRefGoogle Scholar
[2]Loxton, J.H. and Van Der Poorten, A.J., “Miltiplicative dependence in number fields”, Acta Arith. 42 (1983), 291–302.CrossRefGoogle Scholar
[3]Masser, D.W., “Specializations of finitely generated subgroups of abelian varieties”, Trans. Amer. Math. Soc. (to appear).Google Scholar
[4]Pólya, G. and Szegö, G., Problems and Theorems in Analysis I, II, (Springer 1976).Google Scholar
[5]Ritt, J.F., “A factorisation theory for functions , Trans. Amer. Math. Soc. 29 (1927), 584–596.Google Scholar
[6]Rumely, R.S. and Van Der Poorten, A.J., “A note on the Hadamard k-th root of a rational function”, J. Austral. Math. Soc. (to appear).Google Scholar
[7]Van Der Poorten, A.J., “The Hadamard Quotient Theorem for rational functions”, (in preparation).Google Scholar