Abstract
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.
Original language | English (US) |
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Pages (from-to) | 3993-4002 |
Number of pages | 10 |
Journal | Proceedings of the American Mathematical Society |
Volume | 136 |
Issue number | 11 |
DOIs | |
State | Published - Nov 2008 |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics