3 citations · 8 across the 12 of their papers we have counts for
13 papers
-difference analogue of the Stothers-Mason theorem
Jian-Tang Lu, Xing-Xing Lu, Zhi-Tao Wen
In this paper, we give a new definition of the -weight of zeros, which reduces to the multiplicity of zeros as . Furthermore, we obtain a -difference version of the S…
All possible orders less than 1 of transcendental entire solutions of linear difference equations with polynomial coefficients
Katsuya Ishizaki, Zhi-Tao Wen
In this paper, we study all possible orders which are less than 1 of transcendental entire solutions of linear difference equations \begin{equation} P_m(z)Δ^mf(z)+\cdots+P_1(z)Δf(z…
Value distribution of exponential polynomials and their role in the theories of complex differential equations and oscillation theory
Janne Heittokangas, Katsuya Ishizaki, Kazuya Tohge +1
An exponential polynomial is a finite linear sum of terms , where and are polynomials. The early results on the value distribution of exponential polyno…
Dual exponential polynomials and a problem of Ozawa
Janne Heittokangas, Katsuya Ishizaki, Kazuya Tohge +1
Complex linear differential equations with entire coefficients are studied in the situation where one of the coefficients is an exponential polynomial and dominates the growth of a…
Meromorphic functions of finite -order and linear Askey-Wilson divided difference equations
Hui Yu, Janne Heittokangas, Jun Wang +1
The growth of meromorphic solutions of linear difference equations containing Askey-Wilson divided difference operators is estimated. The -order is used as a general growth indi…
Difference radical in terms of shifting zero and applications to the Stothers-Mason theorem
Katsuya Ishizaki, Zhi-Tao Wen
In this paper, we study the shifting zeros with its heights and an analogue to difference radical. We focus on the Stothers-Mason theorem by using falling factorials. As applicatio…
Meromorphic functions of finite -order and linear -difference equations
Janne Heittokangas, Jun Wang, Zhi-Tao Wen +1
The -order was introduced in 2009 for meromorphic functions in the unit disc, and was used as a growth indicator for solutions of linear differential equations. In this paper, t…
Contour integral solutions of linear differential equations which include a generalization of the Airy integral
Gary G. Gundersen, Janne M. Heittokangas, Zhi-Tao Wen
The Airy integral is a well-known contour integral solution of Airy's equation which has several applications and which has been used for mathematical illustrations due to its inte…
A continuous transition from -sets to -sets and beyond
Jie Ding, Janne Heittokangas, Zhi-Tao Wen
The well-known -sets introduced by Hayman in 1960 are collections of Euclidean discs in the complex plane with the following property: The set of angles for which…
The asymptotic number of zeros of exponential sums in critical strips
J. Heittokangas, Z. -T. Wen
Normalized exponential sums are entire functions of the form where $H_1,\ldots, H_n\in\C$ and . It is known that the…
Binomial series and complex difference equations
Katsuya Ishizaki, Zhi-Tao Wen
We consider properties of binomial series , where and the convergence of binomial series in the com…
Deficient values of solutions of linear differential equations
Gary G. Gundersen, Janne Heittokangas, Zhi-Tao Wen
Differential equations of the form (*) are considered, where and are entire functions. The Lindelöf function is used to show t…
Generalization of Pólya's zero distribution theory for exponential polynomials, plus sharp results for asymptotic growth
Janne Heittokangas, Zhi-Tao Wen
An exponential polynomial of order is an entire function of the form where the coefficients are polynomial…