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Unicity theorems for meromorphic or entire functions II

Published online by Cambridge University Press:  17 April 2009

Hong-Xun Yi
Hong-Xun Yi
Affiliation:
Department of Mathematics, Shandong University, Jinan, Shandong 250100, Peoples Republic of China
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Abstract

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In 1976, Gross posed the question “can one find two (or possibly even one) finite sets Sj (j = 1, 2) such that any two entire functions f and g satisfying Ef(Sj) = Eg(Sj) for j = 1,2 must be identical?”, where Ef(Sj) stands for the inverse image of Sj under f. In this paper, we show that there exists a finite set S with 11 elements such that for any two non-constant meromorphic functions f and g the conditions Ef(S) = Eg(S) and Ef({∞}) = Eg({∞}) imply f ≡ g. As a special case this also answers the question posed by Gross.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 2 , October 1995 , pp. 215 - 224
Copyright
Copyright © Australian Mathematical Society 1995

References

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