J. Heittokangas

activity

20192024

most citedDual exponential polynomials and a problem of Ozawa

3 citations · 10 across the 19 of their papers we have counts for

collaborators

Showing 2019Show all

10 papers · 1 filter

math.CV2019

On meromorphic solutions of non-linear differential equations of Tumura-Clunie type

Janne Heittokangas, Zinelaabidine Latreuch, Jun Wang +1

Meromorphic solutions of non-linear differential equations of the form $f^{n} + P (z, f) = h$ are investigated, where $n \geq 2$ is an integer, $h$ is a meromorphic function, and $P (z, f)$ i…

math.CV2019

On the number of linearly independent rapid solutions to linear differential and linear difference equations

Janne Heittokangas, Hui Yu, M. Amine Zemirni

Assuming that $A_{0}, \dots, A_{n - 1}$ are entire functions and that $p \in {0, \dots, n - 1}$ is the smallest index such that $A_{p}$ is transcendental, then, by a classical theorem of Fr…

math.CV2019

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…

math.CV2019★ 1 cited

A continuous transition from $E$ -sets to $R$ -sets and beyond

Jie Ding, Janne Heittokangas, Zhi-Tao Wen

The well-known $E$ -sets introduced by Hayman in 1960 are collections of Euclidean discs in the complex plane with the following property: The set of angles $θ$ for which…

math.CV2019★ 1 cited

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 $f (z) = 1 + H_{1} e^{w_{1} z} + \dots + H_{n} e^{w_{n} z},$ where $H_1,\ldots, H_n\in\C$ and $0 < w_{1} < \dots < w_{n}$ . It is known that the…

math.CV2019★ 1 cited

Deficient values of solutions of linear differential equations

Gary G. Gundersen, Janne Heittokangas, Zhi-Tao Wen

Differential equations of the form $f^{''} + A (z) f^{'} + B (z) f = 0$ (*) are considered, where $A (z)$ and $B (z) \neq \equiv 0$ are entire functions. The Lindelöf function is used to show t…

math.CV2019

Exponential polynomials in the oscillation theory

Janne Heittokangas, Katsuya Ishizaki, Ilpo Laine +1

Supposing that $A (z)$ is an exponential polynomial of the form $A (z) = H_{0} (z) + H_{1} (z) e^{ζ_{1} z^{n}} + \dots + H_{m} (z) e^{ζ_{m} z^{n}},$ where $H_{j}$ 's are entire and of order $< n$ , it is demons…

math.CV2019★ 1 cited

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 $q$ is an entire function of the form $f (z) = P_{1} (z) e^{Q_{1} (z)} + \dots + P_{k} (z) e^{Q_{k} (z)},$ where the coefficients $P_{j} (z), Q_{j} (z)$ are polynomial…

math.CA2019★ 1 cited

Oscillation of solutions of LDE's in domains conformally equivalent to unit disc

Igor Chyzhykov, Janne Gröhn, Janne Heittokangas +1

Oscillation of solutions of $f^{(k)} + a_{k - 2} f^{(k - 2)} + \dots + a_{1} f^{'} + a_{0} f = 0$ is studied in domains conformally equivalent to the unit disc. The results are applied, for e…

math.CA2019

Description of growth and oscillation of solutions of complex LDE's

Igor Chyzhykov, Janne Gröhn, Janne Heittokangas +1

It is known that, equally well in the unit disc as in the whole complex plane, the growth of the analytic coefficients $A_{0}, \dots, A_{k - 2}$ of \begin{equation*} f^{(k)} + A_{k-2} f…

On meromorphic solutions of non-linear differential equations of Tumura-Clunie type

On the number of linearly independent rapid solutions to linear differential and linear difference equations

Contour integral solutions of linear differential equations which include a generalization of the Airy integral

A continuous transition from E-sets to R-sets and beyond

The asymptotic number of zeros of exponential sums in critical strips

Deficient values of solutions of linear differential equations

Exponential polynomials in the oscillation theory

Generalization of Pólya's zero distribution theory for exponential polynomials, plus sharp results for asymptotic growth

Oscillation of solutions of LDE's in domains conformally equivalent to unit disc

Description of growth and oscillation of solutions of complex LDE's

A continuous transition from $E$ -sets to $R$ -sets and beyond