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Arithmetic properties of certain functions in several variables III

Published online by Cambridge University Press:  17 April 2009

J.H. Loxton  and
A.J. van der Poorten
J.H. Loxton
Affiliation:
School of Mathematics, University of New South Wales, Kensington, New South Wales.
A.J. van der Poorten
Affiliation:
School of Mathematics, University of New South Wales, Kensington, New South Wales.
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Abstract

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We obtain a general transcendence theorem for the solutions of a certain type of functional equation. A particular and striking consequence of the general result is that, for any irrational number w, the function

takes transcendental values at all algebraic points α with 0 < |α| < 1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 1 , February 1977 , pp. 15 - 47
Copyright
Copyright © Australian Mathematical Society 1977

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