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Keywords:
meromorphic function; unique range set; weighted shared sets wider sense; linear dependency
meromorphic function; unique range set; weighted shared sets wider sense; linear dependency
Summary:
We comprehensively explore the generalized concept of sharing sets to establish conditions for the linear dependency of two meromorphic functions. By applying this approach, we significantly extend and enhance the existing results related to URSM (unique range set of meromorphic functions). It is well known that URSMs can be represented as zeros of specific polynomials. However, our findings demonstrate that the concept of URSM can be understood from a broader perspective, where it can be characterized as a special case of the zero sets of two interconnected polynomials. Such investigations have not been conducted before, thus the text breaks the barriers of the traditional definition of URSM.
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