325 citations · 362 across the 22 of their papers we have counts for
26 papers
On the extension of analytic solutions of first-order difference equations
Rod Halburd, Risto Korhonen, Yan Liu +1
We will consider first-order difference equations of the form \[ y(z+1) = \frac{λy(z)+a_2(z)y(z)^2+\cdots+a_p(z)y(z)^p}{1 + b_1(z)y(z)+\cdots+b_q(z)y(z)^q}, \] where $λ\in\mathbb{C…
Zero order meromorphic solutions of -difference equations of Malmquist type
Risto Korhonen, Yueyang Zhang
We consider the first order -difference equation \begin{equation}\tag† f(qz)^n=R(z,f), \end{equation} where is a constant and is rational in both arguments.…
A new proximity function estimate on the quotient of the difference and the derivative of a meromorphic function
Lasse Asikainen, Juha-Matti Huusko, Risto Korhonen
It is shown that, under certain assumptions on the growth and value distribution of a meromorphic function , \begin{equation*} m\left(r,\frac{Δ_cf - ac}{f' - a}\right)=S(r,f'…
Tropical second main theorem and the Nevanlinna inverse problem
Juho Halonen, Risto Korhonen, Galina Filipuk
A generalization of the second main theorem of tropical Nevanlinna theory is presented for noncontinuous piecewise linear functions and for tropical hypersurfaces without requiring…
On meromorphic solutions of Malmquist type difference equations
Yueyang Zhang, Risto Korhonen
Recently, the present authors used Nevanlinna theory to provide a classification for the Malmquist type difference equations of the form that have transcend…
A Malmquist--Steinmetz theorem for difference equations
Yueyang Zhang, Risto Korhonen
It is shown that if the equation \begin{equation*} f(z+1)^n=R(z,f), \end{equation*} where is rational in both arguments and , has a transcendental merom…