The dynamics of complex polynomials and automorphisms of the shift.
The effect of the rotation group on the behaviour of a rotation automorphic function.
The entire solutions of a polynomial difference equation.
The Equichordal Point Problem.
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 exponent of convergence of a finite Blaschke product.
The Exponential Map is Not Recurrent.
The extremum problem for analytic functions with finite area integral.
The Fatou and Julia sets of multivalued analytical functions.
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 functional equation F(ax) + F(bx+a) = F(bx) + F(ax+b), entire and almost periodic solutions.
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 geometric means of an entire function of order zero.
The geometric means of an entire function of order zero - II
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 higher derivatives of the inverse tangent function and rapidly convergent BBP-type formulas for pi.
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 Iversen theorem in a polydisc.
The Laguerre inequality and the distribution of zeros of entire functions
The Laguerre inequality and the distribution of zeros of real entire functions are investigated with the aid of certain infinite-order differential operators. The paper includes new proofs, problems, conjectures and many illustrative examples and counterexamples.