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A generalisation of Turán's main theorems to binomials and logarithms

Published online by Cambridge University Press:  17 April 2009

A. J. van der Poorten
A. J. van der Poorten
Affiliation:
University of New South Wales, Kensington, New South Wales.
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Abstract

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The Main Theorems of P. Turán's book Eine neue Methode in der Analysis und deren Anwendungen concern only sums of powers but are easily generalised to exponential sums with polynomial coefficients. It does not appear to have been observed however, that similar such theorems with analogous implication as to value distribution and arithmetical behaviour can be formulated for a wider class of functions. We prove a result for functions of the form subsuming identities which Mahler has shown to contain transcendence results on the exponential and logarithmic functions and diophantine results of the Thue-Siegel-Roth type.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 2 , Issue 2 , April 1970 , pp. 183 - 195
Copyright
Copyright © Australian Mathematical Society 1970

References

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