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 in B or f = q1ep +q2, where p is a polynomial and q1, q2 are rational functions. In the latter case, h/g belongs to the algebra generated by the rational functions, ep and e−p.
Coman, Dan and Poletsky, Evgeny A., "Stable Algebras of Entire Functions" (2007). Mathematics Faculty Scholarship. Paper 19.
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