Tohoku Mathematical Journal
2011

June
SECOND SERIES VOL. 63, NO. 2

Tohoku Math. J.
63 (2011), 149-162

Title SHARED VALUES, PICARD VALUES AND NORMALITY

Author Jianming Chan and Yuefei Wang

(Received November 27, 2009, revised July 12, 2010)
Abstract. It is known that a family of meromorphic functions is normal if each function in the family shares a 3-element set with its derivative. In this paper we consider value distribution and normality problems with regard to 2-element shared sets. First we construct an example, by use of the Weierstrass doubly periodic functions, to show that a 3-element shared set can not be reduced to a 2-element shared set in general. We obtain a new criterion of normal families and new Picard-type theorems. The proofs make use of some results in complex dynamics. More examples are constructed to show that our assumptions are necessary.

2000 Mathematics Subject Classification. Primary 30D45; Secondary 30D35.

Key words and phrases. Meromorphic functions, normality, shared values and sets.

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