ON THE UNIQUENESS THEOREMS OF L-FUNCTIONS CONCERNING WEIGHTED SHARING

N. K. Datta and N. Mandal

  DOI:  https://doi.org/10.37418/amsj.9.11.6

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We mainly study the properties of L-functions using Nevanlinna value distribution theory in the extended selberg class. In this paper, we investigate the relationship between meromorphic functions and L-functions concerning weighted sharing with the help of Nevanlinna value distribution theory. We prove a uniqueness theorem of a meromorphic function and an L-function when they share $(0,0)$ and $(1,1)$. We also get valuable information about the counting of the zeros of L-functions. The results of this paper improve some recent results of W. J. Hao and J. F. Chen \cite{hao18}.

Keywords: Meromorphic functions, L-functions, Weighted sharing, Uniqueness.