Growth numbers of Entire Functions Defined by Dirichlet Series
Growth of coefficients of universal Dirichlet series
We study universal Dirichlet series with respect to overconvergence, which are absolutely convergent in the right half of the complex plane. In particular we obtain estimates on the growth of their coefficients. We can then compare several classes of universal Dirichlet series.
Growth of entire functions with some univalent Gelfond-Leontev derivatives.
Growth of (frequently) hypercyclic functions for differential operators
We investigate the conjugate indicator diagram or, equivalently, the indicator function of (frequently) hypercyclic functions of exponential type for differential operators. This gives insights into growth conditions for these functions on particular rays or sectors. Our research extends known results in several respects.
Growth of meromorphic solutions of higher-order linear differential equations.
Growth of operator valued meromorphic functions.
Growth of polynomials whose zeros are outside a circle
If p(z) be a polynomial of degree n, which does not vanish in |z| < k, k < 1, then it was conjectured by Aziz [Bull. Austral. Math. Soc. 35 (1987), 245-256] that [...] In this paper, we consider the case k < r < 1 and present a generalization as well as improvement of the above inequality.
Growth of polynomials with prescribed zeros
Growth of solutions of a class of complex differential equations
The main purpose of this paper is to partly answer a question of L. Z. Yang [Israel J. Math. 147 (2005), 359-370] by proving that every entire solution f of the differential equation has infinite order and its hyperorder is a positive integer or infinity, where P is a nonconstant entire function of order less than 1/2. As an application, we obtain a uniqueness theorem for entire functions related to a conjecture of Brück [Results Math. 30 (1996), 21-24].
Growth of solutions of certain non-homogeneous linear differential equations with entire coefficients.
Growth of solutions of complex differential equations with coefficients of finite iterated order.
Growth of solutions of higher-order linear differential equations.
Growth of solutions to higher order linear homogeneous differential equations in angular domains.
Growth of solutions to linear differential equations with entire coefficients of slow growth.
Growth of the coefficient auf quasiconformality and the boundary correspondence of automorphisms of a ball.
Growth of the product
We estimate the maximum of on the unit circle where 1 ≤ a₁ ≤ a₂ ≤ ... is a sequence of integers. We show that when is or when is a quadratic in j that takes on positive integer values, the maximum grows as exp(cn), where c is a positive constant. This complements results of Sudler and Wright that show exponential growth when is j. In contrast we show, under fairly general conditions, that the maximum is less than , where r is an arbitrary positive number. One consequence is that the...
Growth results for a subclass of Bazilevich functions.
Growth Theorem and the Radius of Starlikeness of Close-to-Spirallike Functions
AMS Subj. Classification: 30C45
Grunsky coefficient inequalities, Caratheodory metric and extremal quasiconformal mappings.