|
Matematicheskaya Fizika, Analiz, Geometriya [Mathematical Physics, Analysis, Geometry], 1998, Volume 5, Number 3/4, Pages 212–227
(Mi jmag438)
|
|
|
|
This article is cited in 9 scientific papers (total in 9 papers)
An analogue of the second main theorem for uniform metric
I. I. Marchenko Kharkiv State University
Abstract:
Let $f$ be a meromorphic function of finite lower order $\lambda$, and order $\rho$, $T(r,f)$ be Nevanlinna's characteristic, $0<\gamma<\infty$, $B(\gamma)$ be Paley's constant. We obtain the estimates for upper and lower logarithmic density of set
$$
E(\gamma)=\{r:\sum\limits_{k=1}^{q}\log^{+}\max\limits_{|z|=r}|f(z)-a_k|^{-1}<2B(\gamma)T(r,f)\}.
$$
It is shown that
$$
\overline{log dens}E(\gamma)\ge 1-\frac{\lambda}{\gamma}, \quad \underline{log dens}E(\gamma) \ge 1-\frac{\rho}{\gamma}\,.
$$
Received: 30.06.1998
Citation:
I. I. Marchenko, “An analogue of the second main theorem for uniform metric”, Mat. Fiz. Anal. Geom., 5:3/4 (1998), 212–227
Linking options:
https://www.mathnet.ru/eng/jmag438 https://www.mathnet.ru/eng/jmag/v5/i3/p212
|
Statistics & downloads: |
Abstract page: | 153 | Full-text PDF : | 64 |
|