On a property of the Nevanlinna characteristic - Zabolotskyy, M. V.; Zabolotskyy , T. M. (Ukrains’kyi Matematychnyi Zhurnal, 2021)
UDC 517.53We prove the existience of entire functions $f$ of an arbitrary lower order $λ\ge 0$ and the order $ρ=λ+1$ such that \begin{equation*}\underset{r → +∞}{\overline{\lim}}T(r + 1, f)/T(r, f) > 1.\end{equation*}Obtained results show that the condition $ρ - λ < 1$ of Valiron's theorem can not be improved.