Arithmetic properties of certain functions in several variables III

J. H. Loxton; A. J. van der Poorten

doi:10.1017/S0004972700022978

Arithmetic properties of certain functions in several variables III

J. H. Loxton, A. J. van der Poorten

Research output: Contribution to journal › Article

35 Citations (Scopus)

Abstract

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 Î± with 0 < |Î±| < 1.

Original language	English
Pages (from-to)	15-47
Number of pages	33
Journal	Bulletin of the Australian Mathematical Society
Volume	16
Issue number	1
DOIs	https://doi.org/10.1017/S0004972700022978
Publication status	Published - 1977
Externally published	Yes

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title = "Arithmetic properties of certain functions in several variables III",

abstract = "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 {\^I}± with 0 < |{\^I}±| < 1.",

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