We use the theory of normal families to obtain some uniqueness theorems for entire functions, which improve and generalize the related results of Rubel and Yang, and Li and Yi. Some examples are provided to show the sharpness of our results.
We deal with uniqueness of entire functions whose difference polynomials share a nonzero polynomial CM, which corresponds to Theorem 2 of I. Laine and C. C. Yang [Proc. Japan Acad. Ser. A 83 (2007), 148-151] and Theorem 1.2 of K. Liu and L. Z. Yang [Arch. Math. 92 (2009), 270-278]. We also deal with uniqueness of entire functions whose difference polynomials share a meromorphic function of a smaller order, improving Theorem 5 of J. L. Zhang [J. Math. Anal. Appl. 367 (2010), 401-408], where the entire...
This paper is devoted to the study of uniqueness of meromorphic functions sharing only one value or fixed points. We improve some related results due to J. L. Zhang [Comput. Math. Appl. 56 (2008), 3079-3087] and M. L. Fang [Comput. Math. Appl. 44 (2002), 823-831], and we supplement some results given by M. L. Fang and X. H. Hua [J. Nanjing Univ. Math. Biquart. 13 (1996), 44-48] and by C. C. Yang and X. H. Hua [Ann. Acad. Sci. Fenn. Math. 22 (1997), 395-406].
This paper is devoted to value distribution and uniqueness problems for difference polynomials of entire functions such as fⁿ(f-1)f(z+c). We also consider sharing value problems for f(z) and its shifts f(z+c), and improve some recent results of Heittokangas et al. [J. Math. Anal. Appl. 355 (2009), 352-363]. Finally, we obtain some results on the existence of entire solutions of a difference equation of the form
In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.
In this paper we discuss the value distribution problem for -adic meromorphic functions and their derivatives, and prove a generalized version of the Hayman Conjecture for -adic meromorphic functions.
In this paper we introduce the notion of weak normal and quasinormal families of holomorphic curves from a domain in into projective spaces. We will prove some criteria for the weak normality and quasinormality of at most a certain order for such families of holomorphic curves.
In this paper we study the uniqueness for meromorphic functions sharing one value, and obtain some results which improve and generalize the related results due to M. L. Fang, X. Y. Zhang, W. C. Lin, T. D. Zhang, W. R. Lü and others.
Under certain mild analytic assumptions one obtains a lower bound, essentially of order , for the number of zeros and poles of a Dirichlet series in a disk of radius . A more precise result is also obtained under more restrictive assumptions but still applying to a large class of Dirichlet series.