Taiwanese Journal of Mathematics

Unique Range Sets for Meromorphic Functions Constructed without an Injectivity Hypothesis

Ta Thi Hoai An

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Abstract

A set is called a unique range set (counting multiplicities) for a particular family of functions if the inverse image of the set counting multiplicities uniquely determines the function in the family. So far, almost all constructions of unique range sets for meromorphic functions are zero sets of polynomials which satisfy an injectivity condition introduced by Fujimoto. A polynomial $P(z)$ satisfies the injectivity condition if $P$ is injective on the zeros of its derivative. In this paper, we will construct examples of unique range sets for meromorphic functions without assuming an injectivity condition.

Article information

Source
Taiwanese J. Math., Volume 15, Number 2 (2011), 697-709.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406229

Digital Object Identifier
doi:10.11650/twjm/1500406229

Mathematical Reviews number (MathSciNet)
MR2810176

Zentralblatt MATH identifier
1244.30053

Subjects
Primary: 30D30: Meromorphic functions, general theory 30D35: Distribution of values, Nevanlinna theory

Keywords
unique range set uniqueness polynomial functional equation

Citation

An, Ta Thi Hoai. Unique Range Sets for Meromorphic Functions Constructed without an Injectivity Hypothesis. Taiwanese J. Math. 15 (2011), no. 2, 697--709. doi:10.11650/twjm/1500406229. https://projecteuclid.org/euclid.twjm/1500406229


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References

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