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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the unique range set
of meromorphic functions


Authors: Ping Li and Chung-Chun Yang
Journal: Proc. Amer. Math. Soc. 124 (1996), 177-185
MSC (1991): Primary 30D35
MathSciNet review: 1291784
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper studies the unique range set of meromorphic functions and shows that there exists a finite set $S$ such that for any two nonconstant meromorphic functions $f$ and $g$ the condition $E_f(S)=E_g(S)$ implies $f\equiv g$. As a special case this also answers an open question posed by Gross (1977) about entire functions and improves some results obtained recently by Yi.


References [Enhancements On Off] (What's this?)

  • 1 F. Gross, Complex analysis, Lecture Notes in Math., vol. 599, Springer, Berlin and New York, 1977 pp. 51--69
  • 2 Fred Gross and Chung Chun Yang, On preimage and range sets of meromorphic functions, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), no. 1, 17–20. MR 649056 (83d:30027)
  • 3 F. Gross, Factorizations of meromorphic functions, U.S. Government Printing Office Publication, Washington D.C., 1972.
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Additional Information

Ping Li
Affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Chung-Chun Yang
Affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Email: mayang@usthk.bitnet

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03045-6
PII: S 0002-9939(96)03045-6
Keywords: Meromorphic function, entire function, unique range set
Received by editor(s): March 21, 1994
Received by editor(s) in revised form: July 26, 1994
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society