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Algebraic independence properties of the Fredholm series

Published online by Cambridge University Press:  09 April 2009

J. H. Loxton  and
A. J. van der Poorten
J. H. Loxton
Affiliation:
School of Mathematics University of New South WalesKensington New South Wales 2033Australia
A. J. van der Poorten
Affiliation:
School of Mathematics University of New South WalesKensington New South Wales 2033Australia
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Abstract

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We consider algebraic independence properties of series such as We show that the functions fr(z) are algebraically independent over the rational functions Further, if αrs (r = 2, 3, 4, hellip; s = 1, 2, 3, hellip) are algebraic numbers with 0 < |αrs|, we obtain an explicit necessary and sufficient condition for the algebraic independence of the numbers fr(αrs) over the rationals.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 1 , August 1978 , pp. 31 - 45
Copyright
Copyright © Australian Mathematical Society 1978

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