A survey on different uniqueness and strong uniqueness polynomials and their generating unique range sets
Abhijit Banerjee (University of Kalyani, India)
Abstract: The notion of unique range sets was introduced by Gross-Yang [Proc. Japan Acad., 58 (1982), 17-20]. Since the inception of the definition, it became an interesting topic for the researchers to study. In course of time, the research had been shifted to-wards the characterizations of the polynomial backbone of concerned sets. As a result, the uniqueness and strong uniqueness polynomial appeared in the literature and made a lusting impression.
In 2000, H. Fujimoto [H. Fujimoto, On uniqueness of meromorphic functions sharing finite sets, Amer. J. Math., 122 (2000), 1175-1203.] first discovered a special property of a polynomial, called it as “property (H)” which played a vital role in the research of uniqueness and strong uniqueness polynomial.
Within the realm of Nevanlinna theory, we wish to elaborately characterize the existing uniqueness as well as strong uniqueness polynomials, the relation between them and their contribution in forming the unique range sets under relaxed sharing hypothesis. We also wish to discuss the scope for future research and intend to present our humble contribution in this aspect.
complex variablesdynamical systems
Audience: researchers in the topic
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