The Distribution of Values fo Certain Entire and Meromorphic Functions.
The error term in Nevanlinna's second fundamental theorem for holomorphic mappings on coverings.
Se estudia el término de error en el segundo teorema fundamental para las aplicaciones holomorfas F : Y → P1, donde en Y hay definida una aplicación recubridora holomorfa p : Y → C, aplicaciones consideradas por S. Lang and W. Cherry. También se obtiene el lema de la derivada logarítmica para esta clase de funciones que, en particular, contiene la clase de las funciones algebroides. Se demuestra que la estimación obtenida mejora un resultado clásico de Henrik Selberg sobre la derivada logarítmica...
The fixed points and iterated order of some differential polynomials
This paper is devoted to considering the iterated order and the fixed points of some differential polynomials generated by solutions of the differential equation where ,
The generalized Laguerre inequalities and functions in the Laguerre-Pólya class
The principal goal of this paper is to show that the various sufficient conditions for a real entire function, φ(x), to belong to the Laguerre-Pólya class (Definition 1.1), expressed in terms of Laguerre-type inequalities, do not require the a priori assumptions about the order and type of φ(x). The proof of the main theorem (Theorem 2.3) involving the generalized real Laguerre inequalities, is based on a beautiful geometric result, the Borel-Carathédodory Inequality (Theorem 2.1), and on a deep...
The growth of solutions of algebraic differential equations
Suppose that is a meromorphic or entire function satisfying where is a polynomial in all its arguments. Is there a limitation on the growth of , as measured by its characteristic ? In general the answer to this question is not known. Theorems of Gol'dberg, Steinmetz and the author give a positive answer in certain cases. Some illustrative examples are also given.
The hyper-order of solutions of certain linear complex differential equations
We prove some theorems on the hyper-order of solutions of the equation , where Q is an entire function, which is a polynomial or not, and a is an entire function whose order can be larger than 1. We improve some results by J. Wang and X. M. Li.
The improvement of the value distribution on
The range of a random function defined in the unit disk
The second main theorem for algebroid functions.
The singular directions of solutions of some equations.
The value-distribution of lacunary series and a conjecture of Paley
The purpose of this paper is to establish a theorem which answers a conjecture of Paley on the distribution of values of Hadamard lacunary series and which is useful to study the Peano curve property of such series.
The zero distribution and uniqueness of difference-differential polynomials
We consider the zero distribution of difference-differential polynomials of meromorphic functions and present some results which can be seen as the discrete analogues of the Hayman conjecture. In addition, we also investigate the uniqueness of difference-differential polynomials of entire functions sharing one common value. Our theorems improve some results of Luo and Lin [J. Math. Anal. Appl. 377 (2011), 441-449] and Liu, Liu and Cao [Appl. Math. J. Chinese Univ. 27 (2012), 94-104].
Über analytische Funktionen, die im Komplement kleiner Kreisscheiben groß sind.
Über den Verzweigungsindex bei ganzen Funktionen.
Über die Fortsetzung analytischer Funktionen.
Über die logarithmische Ableitung einer algebroiden Funktion.
Über die Nullstellen homogener Differentialpolynome.
Über die Nullstellen meromorpher Funktionen und deren Ableitungen.
Über die Nullstellen von Differentialpolynomen.
Über die Werteverteilung von (f...+...)... .