On a property of the Nevanlinna characteristic

  • M. V. Zabolotskyy Львiв. нац. ун-т iм. I. Франка
  • T. M. Zabolotskyy Львiв. нац. ун-т iм. I. Франка


UDC 517.53
We prove the existience of entire functions $f$ of an arbitrary lower order $\lambda\ge 0$ and the order $\rho=\lambda+1$ such that
\underset{r \to +\infty}{\overline{\lim}}T(r + 1, f)/T(r, f) > 1.
Obtained results show that the condition $\rho - \lambda < 1$ of Valiron's theorem can not be improved.


A. A. Gol`dberg, I. V. Ostrovskij, Raspredelenie znachenij meromorfny`kh funkczij, Moskva, Nauka (1970).

R. Nevanlinna, Analytic function, Springer-Verlag, New York (1970). DOI: https://doi.org/10.1007/978-3-642-85590-0

J. Clunie, On integral functions having prescribed asymptotic growth, Can. J. Math., 17, № 3, 396 – 404 (1965), https://doi.org/10.4153/CJM-1965-040-8 DOI: https://doi.org/10.4153/CJM-1965-040-8

How to Cite
Zabolotskyy, M. V., and T. M. Zabolotskyy. “On a Property of the Nevanlinna Characteristic”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 8, Aug. 2021, pp. 1140 -46, doi:10.37863/umzh.v73i8.6627.
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