Arithmetic Properties of Certain Functions in Several Variables II

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

doi:10.1017/S1446788700020772

Arithmetic Properties of Certain Functions in Several Variables II

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

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

If T = (t_ij) is an n x n matrix with non-negative integer entries, we define a transformation T:Cⁿ →Cⁿ by z’ = Tz where We consider functions f₁(z), … f_p(z) of n complex variables which satisfy functional equations of the form fi(z)=a_if_i(Tz)+b_i(z) (1≤i≤p) and we obtain conditions under which the values of these functions at algebraic points are algebraically independent.

Original language	English
Pages (from-to)	393-408
Number of pages	16
Journal	Journal of the Australian Mathematical Society
Volume	24
Issue number	4
DOIs	https://doi.org/10.1017/S1446788700020772
Publication status	Published - 1977
Externally published	Yes

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title = "Arithmetic Properties of Certain Functions in Several Variables II",

abstract = "If T = (tij) is an n x n matrix with non-negative integer entries, we define a transformation T:Cn →Cn by z{\textquoteright} = Tz where We consider functions f1(z), … fp(z) of n complex variables which satisfy functional equations of the form fi(z)=aifi(Tz)+bi(z) (1≤i≤p) and we obtain conditions under which the values of these functions at algebraic points are algebraically independent.",

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

year = "1977",

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publisher = "Cambridge University Press (CUP)",

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T1 - Arithmetic Properties of Certain Functions in Several Variables II

AU - Loxton, J. H.

AU - van der Poorten, A. J.

PY - 1977

Y1 - 1977

N2 - If T = (tij) is an n x n matrix with non-negative integer entries, we define a transformation T:Cn →Cn by z’ = Tz where We consider functions f1(z), … fp(z) of n complex variables which satisfy functional equations of the form fi(z)=aifi(Tz)+bi(z) (1≤i≤p) and we obtain conditions under which the values of these functions at algebraic points are algebraically independent.

AB - If T = (tij) is an n x n matrix with non-negative integer entries, we define a transformation T:Cn →Cn by z’ = Tz where We consider functions f1(z), … fp(z) of n complex variables which satisfy functional equations of the form fi(z)=aifi(Tz)+bi(z) (1≤i≤p) and we obtain conditions under which the values of these functions at algebraic points are algebraically independent.

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U2 - 10.1017/S1446788700020772

DO - 10.1017/S1446788700020772

M3 - Article

AN - SCOPUS:84974466054

SN - 1446-7887

VL - 24

SP - 393

EP - 408

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 4

ER -

Arithmetic Properties of Certain Functions in Several Variables II

Abstract

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