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December 2020 On the existence of unique range sets generated by non-critically injective polynomials and related issues
Sanjay Mallick
Tbilisi Math. J. 13(4): 81-101 (December 2020). DOI: 10.32513/tbilisi/1608606051

Abstract

In this paper, we prove the existence of non-critically injective polynomials whose set of zeros form unique range sets that answers one of the most awaited and fundamental questions of uniqueness theory of entire and meromorphic functions. We also show that there exist some unique range sets and their generating polynomials which can not be characterized by any of the existing generalized results of unique range sets but as an application of our main theorems the same can be characterized. Moreover, as an application of our main results we prove that the cardinality of a unique range set does not always depend upon the number of distinct critical points of its generating polynomial.

Citation

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Sanjay Mallick. "On the existence of unique range sets generated by non-critically injective polynomials and related issues." Tbilisi Math. J. 13 (4) 81 - 101, December 2020. https://doi.org/10.32513/tbilisi/1608606051

Information

Received: 16 April 2020; Accepted: 22 September 2020; Published: December 2020
First available in Project Euclid: 22 December 2020

MathSciNet: MR4194230
Digital Object Identifier: 10.32513/tbilisi/1608606051

Subjects:
Primary: 30D35

Rights: Copyright © 2020 Tbilisi Centre for Mathematical Sciences

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Vol.13 • No. 4 • December 2020
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