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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the unique range set of meromorphic functions
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by Ping Li and Chung-Chun Yang
Proc. Amer. Math. Soc. 124 (1996), 177-185
DOI: https://doi.org/10.1090/S0002-9939-96-03045-6
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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
  • F. Gross, Complex analysis, Lecture Notes in Math., vol. 599, Springer, Berlin and New York, 1977 pp. 51–69
  • 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
  • F. Gross, Factorizations of meromorphic functions, U.S. Government Printing Office Publication, Washington D.C., 1972.
  • W. K. Hayman, On the characteristic of functions meromorphic in the unit disk and of their integrals, Acta Math. 112 (1964), 181–214. MR 168763, DOI 10.1007/BF02391770
  • Chung Chun Yang, On deficiencies of differential polynomials. II, Math. Z. 125 (1972), 107–112. MR 294642, DOI 10.1007/BF01110921
  • Hongxun Yi, On a problem of Gross, Sci. China Ser. A 11 (24) (1994), 1137–1144.
  • Hong Xun Yi, Meromorphic functions that share three values, Chinese Ann. Math. Ser. A 9 (1988), no. 4, 434–439 (Chinese). MR 996921
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Bibliographic 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
  • Received by editor(s): March 21, 1994
  • Received by editor(s) in revised form: July 26, 1994
  • Communicated by: Albert Baernstein II
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 177-185
  • MSC (1991): Primary 30D35
  • DOI: https://doi.org/10.1090/S0002-9939-96-03045-6
  • MathSciNet review: 1291784