Suppose that h and g belong to the algebra B generated by the rational functions and an entire function f of finite order on ℂn and that h/g has algebraic polar variety. We show that either h/g ∈ B or f = q1ep + q2, where p is a polynomial and q 1,q2 are rational functions. In the latter case, h/g belongs to the algebra generated by the rational functions, ep and e-p. The stability property is related to the problem of algebraic dependence of entire functions over the ring of polynomials. The case of algebraic dependence over ℂ of two entire or meromorphic functions on ℂn is completely resolved in this paper.
ASJC Scopus subject areas
- Applied Mathematics