Zobrazeno 1 - 10
of 139
pro vyhledávání: '"Korhonen, Risto"'
In 1985, W.K.Hayman (Bayer. Akad. Wiss. Math.-Natur. Kl. Sitzungsber, 1984(1985), 1-13.) proved that there do not exist non-constant meromorphic functions $f,$ $g$ and $h$ satisfying the functional equation $f^n+g^n+h^n=1$ for $n\geq 9.$ We prove tha
Externí odkaz:
http://arxiv.org/abs/2411.01509
Autor:
Korhonen, Risto, Zhang, Yueyang
We consider the first order $q$-difference equation \begin{equation}\tag{\dag} f(qz)^n=R(z,f), \end{equation} where $q\not=0,1$ is a constant and $R(z,f)$ is rational in both arguments. When $|q|\not=1$, we show that, if $(\dag)$ has a zero order tra
Externí odkaz:
http://arxiv.org/abs/2405.03936
It is shown that, under certain assumptions on the growth and value distribution of a meromorphic function $f(z)$, \begin{equation*} m\left(r,\frac{\Delta_cf - ac}{f' - a}\right)=S(r,f'), \end{equation*} where $\Delta_c f=f(z+c)-f(z)$ and $a,c\in\mat
Externí odkaz:
http://arxiv.org/abs/2306.06729
A generalization of the second main theorem of tropical Nevanlinna theory is presented for noncontinuous piecewise linear functions and for tropical hypersurfaces without requiring a growth condition. The method of proof is novel and significantly mo
Externí odkaz:
http://arxiv.org/abs/2305.13939
Autor:
Zhang, Yueyang, Korhonen, Risto
Recently, the present authors used Nevanlinna theory to provide a classification for the Malmquist type difference equations of the form $f(z+1)^n=R(z,f)$ $(\dag)$ that have transcendental meromorphic solutions, where $R(z,f)$ is rational in both arg
Externí odkaz:
http://arxiv.org/abs/2302.05202
Autor:
Zhang, Yueyang1 (AUTHOR), Korhonen, Risto2 (AUTHOR) risto.korhonen@uef.fi
Publikováno v:
Constructive Approximation. Jun2024, Vol. 59 Issue 3, p619-673. 55p.
Autor:
Korhonen, Risto, Zhang, Yueyang
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 December 2024 540(1)
Autor:
Zhang, Yueyang, Korhonen, Risto
It is shown that if the equation \begin{equation*} f(z+1)^n=R(z,f), \end{equation*} where $R(z,f)$ is rational in both arguments and $\deg_f(R(z,f))\not=n$, has a transcendental meromorphic solution, then the equation above reduces into one out of se
Externí odkaz:
http://arxiv.org/abs/2108.06085
Publikováno v:
In Bulletin des sciences mathématiques February 2023 182
Autor:
Zheng, Jianhua, Korhonen, Risto
This paper consists of three parts. First, we give so far the best condition under which the shift invariance of the counting function, and of the characteristic of a subharmonic function, holds. Second, a difference analogue of logarithmic derivativ
Externí odkaz:
http://arxiv.org/abs/1806.00212