UNIQUENESS RESULTS ON DIFFERENTIAL POLYNOMIALS GENERATED BY A MEROMORPHIC FUNCTION AND A L-FUNCTION

Raj, Preetham N; Waghamore, Harina P.

doi:10.21608/ejmaa.2023.206074.1028

UNIQUENESS RESULTS ON DIFFERENTIAL POLYNOMIALS GENERATED BY A MEROMORPHIC FUNCTION AND A L-FUNCTION

Document Type : Regular research papers

Authors

¹ Department of mathematics, Bangalore University, Janabharathi Campus, Bangalore, India

² Departrment of Mathematics, Bangalore University, Jnanabharathi Campus, Bengaluru, Karnataka, India

10.21608/ejmaa.2023.206074.1028

Abstract

The Riemann zeta function and its various generalizations have been extensively studied by mathematicians worldwide. The L-functions are Selberg class functions with Riemann zeta function as the prototype and since L-functions are analytically continued as meromorphic functions, it is convenient to study the value distribution and uniqueness problems on L-functions and arbitrary meromorphic functions. Further, the fact that L-functions neither have a pole nor zero at the origin, but is having only possible pole at s = 1 helps us to study some of the classical results of Boussaf et al. [3] in terms of an L-function and an arbitrary meromorphic function. In this paper, by using the concept of weighted sharing and least multiplicity, we study the value distribution of an L-function and an arbitrary meromorphic function when certain type of differential polynomials generated by them share a non-zero small function with finite weight. Our results extends and improves some of the classical results due to Boussaf et al. (Indagationes Mathematicae 24(1):15-41, 2013).

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