THE BRÜCK CONJECTURE AND ENTIRE FUNCTIONS SHARING POLYNOMIALS WITH THEIR κ-TH DERIVATIVES

- Journal title : Journal of the Korean Mathematical Society
- Volume 48, Issue 3, 2011, pp.499-512
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2011.48.3.499

Title & Authors

THE BRÜCK CONJECTURE AND ENTIRE FUNCTIONS SHARING POLYNOMIALS WITH THEIR κ-TH DERIVATIVES

Lu, Feng; Yi, Hongxun;

Lu, Feng; Yi, Hongxun;

Abstract

The purpose of this paper is twofold. The first is to establish a uniqueness theorem for entire function sharing two polynomials with its -th derivative, by using the theory of normal families. Meanwhile, the theorem generalizes some related results of Rubel and Yang and of Li and Yi. Several examples are provided to show the conditions are necessary. The second is to generalize the Br-ck conjecture with the idea of sharing polynomial.

Keywords

Vandermonde determinant;entire functions;Nevanlinna theory;uniqueness;normal family;differential equation;

Language

English

Cited by

1.

ON THE TRANSCENDENTAL ENTIRE SOLUTIONS OF A CLASS OF DIFFERENTIAL EQUATIONS,;;;

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