Arithmetic properties of certain functions in several variables

AbstractIf T is an n × n matrix with nonnegative integral entries, we define a transformation T: Cn → Cn by w = Tz where W1=∏j=1nzjtij (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