Arithmetic properties of certain functions in several variables

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


If T is an n × n matrix with nonnegative integral entries, we define a transformation T: Cn → Cn by w = Tz where W1= ∏ j=1 nzj tij (1≤i≤n). We consider functions f(z) of n complex variables which satisfy a functional equation giving f(Tz) as a rational function of 1f(z) and we obtain conditions under which such a function f(z) takes transcendental values at algebraic points.

Original languageEnglish
Pages (from-to)87-106
Number of pages20
JournalJournal of Number Theory
Issue number1
Publication statusPublished - 1977
Externally publishedYes


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