Growth of meromorphic solutions of higher-order linear differential equations.
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 linear differential equations with entire coefficients of slow growth.
Horizontal sections of connections on curves and transcendence
Let K be a number field, X be a smooth projective curve over it and D be a reduced divisor on X. Let (E,∇) be a vector bundle with connection having meromorphic singularities on D. Let and (the ’s may be in the support of D). Using tools from Nevanlinna theory and formal geometry, we give the definition of E-section of arithmetic type of the vector bundle E with respect to the points ; this is the natural generalization of the notion of E-function defined in Siegel-Shidlovskiĭ theory. We prove...
Hyper-order and order of meromorphic functions sharing functions
In this paper we mainly estimate the hyper-order of an entire function which shares one function with its derivatives. Some examples are given to show that the conclusions are meaningful.
Inequalities arising out of the value distribution of a differential monomial.
Investigations on unique range sets of meromorphic functions in an angular domain
We study unique range sets of meromorphic functions over an angular domain in the light of weighted sharing. One of our main results generalizes and improves a result of Xu et al. (2014). Most importantly, we have pointed out a gap in the proofs of some main results of Rathod (2021) and subsequently rectifying the gap we have conveniently improved the results.
Iterated order of solutions of certain linear differential equations with entire coefficients.
Iterated order of solutions of linear differential equations with entire coefficients.
Iteration, level sets, and zeros of derivatives of meromorphic functions.
Julia lines of general random Dirichlet series
In this paper, we consider a random entire function defined by a random Dirichlet series where are independent and complex valued variables, . We prove that under natural conditions, for some random entire functions of order zero almost surely every horizontal line is a Julia line without an exceptional value. The result improve a theorem of J. R. Yu: Julia lines of random Dirichlet series. Bull. Sci. Math. 128 (2004), 341–353, by relaxing condition on the distribution of for such function...
Linear differential polynomials sharing the same 1-points with weight two
We prove a uniqueness theorem for meromorphic functions involving differential polynomials which improves some previous results and provides a better answer to a question of C. C. Yang.
Linear differential polynomials sharing three values with finite weight.
Linear differential polynomials sharing three values with weights.
Majorations effectives
Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen.
Meromorphic function sharing a small function with a linear differential polynomial
The problem of uniqueness of an entire or a meromorphic function when it shares a value or a small function with its derivative became popular among the researchers after the work of Rubel and Yang (1977). Several authors extended the problem to higher order derivatives. Since a linear differential polynomial is a natural extension of a derivative, in the paper we study the uniqueness of a meromorphic function that shares one small function CM with a linear differential polynomial, and prove the...