Exceptional Sets for Certain Differential Polynomials of Entire Functions

2005 ◽  
Vol 5 (1) ◽  
pp. 153-158
Author(s):  
Guy F. Kendall
Keyword(s):  
Entire Functions ◽  
Differential Polynomials ◽  
Exceptional Sets

ON EXCEPTIONAL SETS: THE SOLUTION OF A PROBLEM POSED BY K. MAHLER

2016 ◽  
Vol 94 (1) ◽  
pp. 15-19 ◽  
Author(s):  
DIEGO MARQUES ◽  
JOSIMAR RAMIREZ
Keyword(s):  
Entire Functions ◽  
Complex Conjugation ◽  
Exceptional Set ◽  
Exceptional Sets ◽  
Transcendental Numbers ◽  
Lecture Notes ◽  
Transcendental Entire Functions

In this paper, we shall prove that any subset of $\overline{\mathbb{Q}}$, which is closed under complex conjugation, is the exceptional set of uncountably many transcendental entire functions with rational coefficients. This solves an old question proposed by Mahler [Lectures on Transcendental Numbers, Lecture Notes in Mathematics, 546 (Springer, Berlin, 1976)].

scholarly journals Uniqueness of difference-differential polynomials of entire functions sharing one value

2016 ◽  
Vol 47 (2) ◽  
pp. 193-206
Author(s):  
Renukadevi S. Dyavanal ◽  
Ashwini M. Hattikal
Keyword(s):  
Entire Functions ◽  
Differential Polynomials ◽  
Counting Multiplicity

In this paper, we study the uniqueness of difference-differential polynomials of entire functions $f$ and $g$ sharing one value with counting multiplicity. In this paper we extend and generalize the results of X. Y. Zhang, J. F. Chen and W. C. Lin [17] L. Kai, L. Xin-ling and C. Ting-bin [7] and many others [2, 16].

scholarly journals Relation between Small Functions with Differential Polynomials Generated by Solutions of Linear Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Zhigang Huang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Entire Functions ◽  
Linear Differential Equations ◽  
Differential Polynomials ◽  
Small Functions ◽  
Linear Differential ◽  
The Relationship ◽  
Growth Of Solutions

This paper is devoted to studying the growth of solutions of second-order nonhomogeneous linear differential equation with meromorphic coefficients. We also discuss the relationship between small functions and differential polynomialsL(f)=d2f″+d1f′+d0fgenerated by solutions of the above equation, whered0(z),d1(z),andd2(z)are entire functions that are not all equal to zero.

scholarly journals Uniqueness of meromorphic functions concerning differential polynomials

2012 ◽  
Vol 43 (1) ◽  
pp. 51-68
Author(s):  
Subhas S. Bhoosnurmath ◽  
Veena L. Pujari ◽  
Anupama J. Patil
Keyword(s):  
Meromorphic Functions ◽  
Simple Technique ◽  
Entire Functions ◽  
Differential Polynomials ◽  
Additional Insight ◽  
Insight Into

In this paper, we present a different and very simple technique to handle various uniqueness problems involving three small entire functions. It also gives a new additional insight into such problems.

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