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

Title & Authors
THE BRÜCK CONJECTURE AND ENTIRE FUNCTIONS SHARING POLYNOMIALS WITH THEIR κ-TH DERIVATIVES
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 $\small{{\kappa}}$-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$\small{\}$$\small{"}$$\small{{u}}$-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,;;;

대한수학회보, 2014. vol.51. 5, pp.1281-1289
2.
A RESULT ON A CONJECTURE OF W. LÜ, Q. LI AND C. YANG,;

대한수학회보, 2016. vol.53. 2, pp.411-421
1.
ON THE TRANSCENDENTAL ENTIRE SOLUTIONS OF A CLASS OF DIFFERENTIAL EQUATIONS, Bulletin of the Korean Mathematical Society, 2014, 51, 5, 1281
2.
A RESULT ON A CONJECTURE OF W. LÜ, Q. LI AND C. YANG, Bulletin of the Korean Mathematical Society, 2016, 53, 2, 411
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