Arithmetic properties of certain functions in several variables

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

doi:10.1016/0022-314X(77)90053-1

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 journal › Article › peer-review

10 Citations (Scopus)

Abstract

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 nz_j ^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 language	English
Pages (from-to)	87-106
Number of pages	20
Journal	Journal of Number Theory
Volume	9
Issue number	1
DOIs	https://doi.org/10.1016/0022-314X(77)90053-1
Publication status	Published - 1977
Externally published	Yes

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

abstract = "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.",

author = "Loxton, {J. H.} and {van der Poorten}, {A. J.}",

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AU - Loxton, J. H.

AU - van der Poorten, A. J.

PY - 1977

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AB - 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.

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U2 - 10.1016/0022-314X(77)90053-1

DO - 10.1016/0022-314X(77)90053-1

M3 - Article

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VL - 9

SP - 87

EP - 106

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -

Arithmetic properties of certain functions in several variables

Abstract

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