Abstract

This study investigates the uniqueness properties of L-functions associ ated with meromorphic functions that share a small function of finite weight. Based on the Value Distribution Theory of Nevanlinna and the uniqueness properties of L-functions, we establish several theorems that demonstrate the conditions under which two L-functions can be considered equivalent, particularly in the context of their shared values and the behavior of associated polynomials. Our results extend, generalize, and improve those of Mandal and Datta [10]. We also provide an ex ample that supports our results and poses open questions regarding the relaxation of conditions in uniqueness theorems.

Keywords and Phrases

Uniqueness, Meromorphic function, difference-differential polynomial, L-function, Set sharing, Small function.

A.M.S. subject classification

30D35

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