Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Stable algebras of entire functions
HTML articles powered by AMS MathViewer

by Dan Coman and Evgeny A. Poletsky PDF
Proc. Amer. Math. Soc. 136 (2008), 3993-4002 Request permission

Abstract:

Suppose that $h$ and $g$ belong to the algebra $\mathcal {B}$ generated by the rational functions and an entire function $f$ of finite order on $\mathbb {C}^n$ and that $h/g$ has algebraic polar variety. We show that either $h/g\in \mathcal {B}$ or $f=q_1e^p+q_2$, where $p$ is a polynomial and $q_1,q_2$ are rational functions. In the latter case, $h/g$ belongs to the algebra generated by the rational functions, $e^p$ 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 $\mathbb {C}$ of two entire or meromorphic functions on $\mathbb {C}^n$ is completely resolved in this paper.

References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32A38, 30H05
  • Retrieve articles in all journals with MSC (2000): 32A38, 30H05
Additional Information
  • Dan Coman
  • Affiliation: Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244-1150
  • MR Author ID: 325057
  • Email: dcoman@syr.edu
  • Evgeny A. Poletsky
  • Affiliation: Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244-1150
  • MR Author ID: 197859
  • Email: eapolets@syr.edu
  • 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
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3993-4002
  • MSC (2000): Primary 32A38; Secondary 30H05
  • DOI: https://doi.org/10.1090/S0002-9939-08-09393-3
  • MathSciNet review: 2425740