UNIQUENESS RESULTS ON DIFFERENTIAL POLYNOMIALS GENERATED BY A MEROMORPHIC FUNCTION AND A L-FUNCTION | ||||
| Electronic Journal of Mathematical Analysis and Applications | ||||
| Volume 11, Issue 2, July 2023, Page 1-17 PDF (555 K) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/ejmaa.2023.206074.1028 | ||||
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| Authors | ||||
Preetham N Raj  1; Harina P. Waghamore2
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| 1Department of mathematics, Bangalore University, Janabharathi Campus, Bangalore, India | ||||
| 2Departrment of Mathematics, Bangalore University, Jnanabharathi Campus, Bengaluru, Karnataka, India | ||||
| 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). | ||||
| Keywords | ||||
| Nevanlinna theory; Weighted sharing; Differential polynomials; Value sharing; p-Adic analysis | ||||
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