Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 15, Number 2 (2011), 697-709.
Unique Range Sets for Meromorphic Functions Constructed without an Injectivity Hypothesis
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.
Taiwanese J. Math., Volume 15, Number 2 (2011), 697-709.
First available in Project Euclid: 18 July 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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