Hostname: page-component-7dd5485656-j7khd Total loading time: 0 Render date: 2025-10-31T14:39:57.956Z Has data issue: false hasContentIssue false
  • English
  • Français

On uniqueness polynomials for meromorphic functions

Published online by Cambridge University Press:  22 January 2016

Hirotaka Fujimoto
Hirotaka Fujimoto*
Affiliation:
Department of Mathematics, Faculty of Science, Kanazawa University, Kanazawa, 920-1192, Japan, fujihiro@beach.ocn.ne.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A polynomial P(w) is called a uniqueness polynomial (or a uiqueness polynomial in a broad sense) if P(f) = cP(g) (or P(f) = P(g)) implies f = g for any nonzero constant c and nonconstant meromorphic functions f and g on C. We consider a monic polynomial P(w) without multiple zero whose derivative has mutually distinct k zeros ej with multiplicities qj. Under the assumption that P(el) ≠ P(em) for all distinct l and m, we prove that P(w) is a uniqueness polynomial in a broad sense if and only if ∑l<mqlqm > ∑l ql. We also give some sufficient conditions for uniqueness polynomials.

Keywords

30D35

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 170 , 2003 , pp. 33 - 46
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

References

[1] Fujimoto, H., On uniqueness of meromorphic functions sharing finite sets, Amer. J. Math., 122 (2000), 1175–1203.Google Scholar
[2] Fulton, W., Algebraic curves, W. A. Benjamin, New York, 1969.Google Scholar
[3] Frank, G. and Reinders, M., A unique range set for meromorphic functions with 11 elements, Complex Variables, 37 (1998), 185–193.Google Scholar
[4] Gross, F. and Yang, C. C., On preimage and range sets of meromorphic functions, Proc. Japan Acad., 58 (1982), 17–20.Google Scholar
[5] Li, P. and Yang, C. C., Some further results on the unique range sets of meromorphic functions, Kodai Math. J., 18 (1995), 437–450.Google Scholar
[6] Miranda, R., Algebraic curves and Riemann surfaces, Amer. Math. Soc., 1995.Google Scholar
[7] Shiffman, B., Uniqueness of entire and meromorphic functions sharing finite sets, Complex Variables, 43 (2001), 433–449.Google Scholar
[8] Yang, C. C. and Hua, X., Unique polynomials of entire and meromorphic functions, Matematicheskaya fizika, analiz, geometriya, 3 (1997), 391–398.Google Scholar
[9] Yi, H., The unique range sets of entire or meromorphic functions, Complex Variables, 28 (1995), 13–21.Google Scholar
[10] Yi, H., Some further results on uniqueness of meromorphic functions, Complex Var-ialbles, 38 (1999), 375–385.Google Scholar