Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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UNIQUENESS THEOREMS OF MEROMORPHIC FUNCTIONS OF A CERTAIN FORM

  • Xu, Junfeng (Department of Mathematics Wuyi University) ;
  • Han, Qi (Department of Mathematics University of Houston) ;
  • Zhang, Jilong (LMIB and Department of Mathematics Beihang University)
  • Published : 2009.11.30
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Abstract

In this paper, we shall show that for any entire function f, the function of the form $f^m(f^n$ - 1)f' has no non-zero finite Picard value for all positive integers m, n ${\in}\;{\mathbb{N}}$ possibly except for the special case m = n = 1. Furthermore, we shall also show that for any two nonconstant meromorphic functions f and g, if $f^m(f^n$-1)f' and $g^m(g^n$-1)g' share the value 1 weakly, then f $\equiv$ g provided that m and n satisfy some conditions. In particular, if f and g are entire, then the restrictions on m and n could be greatly reduced.

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