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UNIQUENESS THEOREMS OF MEROMORPHIC FUNCTIONS OF A CERTAIN FORM

Xu, Junfeng;Han, Qi;Zhang, Jilong

  • Published : 2009.11.30

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.

Keywords

entire function;meromorphic function;Picard value

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  2. Uniqueness Theorems on Difference Monomials of Entire Functions vol.2012, 2012, https://doi.org/10.1155/2012/407351