Stable algebras of entire functions

Authors:
Dan Coman and Evgeny A. Poletsky

Journal:
Proc. Amer. Math. Soc. **136** (2008), 3993-4002

MSC (2000):
Primary 32A38; Secondary 30H05

Published electronically:
June 11, 2008

MathSciNet review:
2425740

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that and belong to the algebra generated by the rational functions and an entire function of finite order on and that has algebraic polar variety. We show that either or , where is a polynomial and are rational functions. In the latter case, belongs to the algebra generated by the rational functions, and .

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 of two entire or meromorphic functions on is completely resolved in this paper.

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Additional Information

**Dan Coman**

Affiliation:
Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244-1150

Email:
dcoman@syr.edu

**Evgeny A. Poletsky**

Affiliation:
Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244-1150

Email:
eapolets@syr.edu

DOI:
https://doi.org/10.1090/S0002-9939-08-09393-3

Received by editor(s):
April 11, 2007

Received by editor(s) in revised form:
October 18, 2007

Published electronically:
June 11, 2008

Additional Notes:
Both authors are supported by NSF Grants.

Communicated by:
Mei-Chi Shaw

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.