Factorization Of Meromorphic Functions Research Articles

Dirichlet series satisfying a Riemann type functional equation and sharing one set

In 2011, Li [A uniqueness theorem for Dirichlet series satisfying a Riemann type functional equation. Adv Math. 2011;226(5):4198–4211] proved that if two L-functions and satisfy the same functional equation with and for two distinct finite complex numbers and then We prove that if two L-functions and have positive degree and satisfy the same functional equation with and for a finite set where and are three distinct finite complex values, then The main results of this paper are concerning some questions posed by Gross [Factorization of meromorphic functions and some open problems. Complex Analysis, Kentucky 1976 (Proc.Conf.); Berlin: Springer-Verlag; 1977. p. 51–69. (Lecture Notes in Mathematics; 599)].

Value distribution of L-functions and uniqueness questions of F. Gross*

We study the value distribution of L-functions and uniqueness questions of meromorphic functions sharing one or two sets with L-functions. The results in this paper extend the corresponding results from [J. Steuding, Value Distribution of L-Functions, Lect. Notes Math., Vol. 1877, Springer-Verlag, Berlin, Heidelberg, 2007, p. 152] and [B.Q. Li, A result on value distribution of L-functions, Proc. Am. Math. Soc., 138(6):2071–2077, 2010]. The studied questions in this paper are related to the questions of Gross from [F. Gross, Factorization of meromorphic functions and some open problems, in Complex Analysis, Kentucky 1976. Proceedings of the Conference Held at the University of Kentucky, May 18–22, 1976, Lect. Notes Math., Vol. 599, Springer-Verlag, Berlin, Heidelberg, 1977, pp. 51–69]. Here the meromorphic functions are of finitely many poles in the complex plane.

On a question of Gross

Using the notion of weighted sharing of sets we prove two uniqueness theorems which improve the results proved by Fang and Qiu [H. Qiu, M. Fang, A unicity theorem for meromorphic functions, Bull. Malaysian Math. Sci. Soc. 25 (2002) 31–38], Lahiri and Banerjee [I. Lahiri, A. Banerjee, Uniqueness of meromorphic functions with deficient poles, Kyungpook Math. J. 44 (2004) 575–584] and Yi and Lin [H.X. Yi, W.C. Lin, Uniqueness theorems concerning a question of Gross, Proc. Japan Acad. Ser. A 80 (2004) 136–140] and thus provide an answer to the question of Gross [F. Gross, Factorization of meromorphic functions and some open problems, in: Proc. Conf. Univ. Kentucky, Lexington, KY, 1976, in: Lecture Notes in Math., vol. 599, Springer, Berlin, 1977, pp. 51–69], under a weaker hypothesis.

On factorization of meromorphic functions

This paper improves on the results of Noda, Y., Li Baoqing and Song Quodong, and proves the following theorem: Letf(z) be a transcendental meromorphic function. Then the set {a∈C;(z−a)f(z) is not prime} is at most a countable set.

Malmquist type theorem and factorization of meromorphic solutions of partial differential equations

In this paper, a general definition of factorization of meromorphic functions of several variables is given. We have proved a general Malmquist type theorem of partial differential equations and prove the pseudo-prime ness of meromorphic solutions of system of Riccati partial differential equations with polynomial coefficients. Also it is proved that any finite order meromorphic solution of linear partial differential equations with rational coefficients must be pseudo-prime. The main tool used in the paper is Nevanlinna type of higher-dimensional value distribution theory.

On Goldbach problem concerning factorization of meromorphic functions

The authors prove in this paper the following Letf (Z) be any transcendental meromorphic function in the plane. Then for any given non-constant fractional linear functionϕ (Z), the set $$\left\{ {a \in \mathbb{C}:f(Z) + a\varphi (Z) is not prime} \right\}$$ is at most a countable set.

The Fix-Points and Factorization of Meromorphic Functions

In this paper, we use the Nevanlinna theory of meromorphic functions and a result of Goldstein to generalize some known results in factorization and fixpoints of entire functions. Specifically, we prove (1) If $f$ and $g$ are nonlinear entire functions such that $f(g)$ is transcendental and of finite order, then $f(g)$ has infinitely many fix-points. (2) If $f$ is a polynomial of degree $\geqq 3$, and $g$ is an arbitrary transcendental meromorphic function, then $f(g)$ must have infinitely many fix-points. (3) Let $p(z),q(z)$ be any nonconstant polynomials, at least one of which is not $c$-even, and let $a$ and $b$ be any constants with $a$ or $b \ne 0$. Then $h(z) = q(z)\exp (a{z^2} + bz) + p(z)$ is prime.

The fix-points and factorization of meromorphic functions

In this paper, we use the Nevanlinna theory of meromorphic functions and a result of Goldstein to generalize some known results in factorization and fixpoints of entire functions. Specifically, we prove (1) If f f and g g are nonlinear entire functions such that f ( g ) f(g) is transcendental and of finite order, then f ( g ) f(g) has infinitely many fix-points. (2) If f f is a polynomial of degree ≧ 3 \geqq 3 , and g g is an arbitrary transcendental meromorphic function, then f ( g ) f(g) must have infinitely many fix-points. (3) Let p ( z ) , q ( z ) p(z),q(z) be any nonconstant polynomials, at least one of which is not c c -even, and let a a and b b be any constants with a a or b ≠ 0 b \ne 0 . Then h ( z ) = q ( z ) exp ⁡ ( a z 2 + b z ) + p ( z ) h(z) = q(z)\exp (a{z^2} + bz) + p(z) is prime.

On Factorization of Meromorphic Functions

On Factorization of Meromorphic Functions

On factorization of meromorphic functions

On factorization of meromorphic functions

Some theorems on factorization of meromorphic functions

Some theorems on factorization of meromorphic functions