Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2018; 33(2): 495-505

Online first article April 12, 2018      Printed April 30, 2018

https://doi.org/10.4134/CKMS.c170170

Copyright © The Korean Mathematical Society.

An entire function sharing a polynomial with linear differential polynomials

Goutam Kumar Ghosh

Dr. Bhupendra Nath Dutta Smriti Mahavidyalaya(The University of Burdwan)

Abstract

The uniqueness problems on entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results on this topic have been obtained. In this paper, we study an entire function $f(z)$ that shares a nonzero polynomial $a(z)$ with $f^{(1)}(z)$, together with its linear differential polynomials of the form: $L=L(f)=a_{1}(z)f^{(1)}(z)+a_{2}(z)f^{(2)}(z)+\cdots+a_{n}(z)f^{(n)}(z)$, where the coefficients $a_{k}(z) (k=1,2,\ldots,n)$ are rational functions and $a_{n}(z)\not\equiv 0$.

Keywords: entire function, rational function, uniqueness

MSC numbers: 30D35