Equivalence of two classes of meromorphic functions (in Ukrainian)

M. Zabolotskyy

It is shown that for every meromorphic in $\Bbb C$ function $f$ with $T(2r,f)\sim T(r,f)$, $r\to\infty$ we have $$ r\smallint_r^{+\infty}\frac{n(t,a,f)}{t^2}dt=o(T(r,f)),\; r\to\infty. $$ for each $a \in \hat {\Bbb C}$. Conversely, if the last condition holds for two values $a,b\in \hat {\Bbb C}$ and $f$ is of genus zero, then $T(2r,f)\sim T(r,f)$, $r\to\infty$.

1. Гольдберг А.А., Островский И.В. Распределение значений мероморфных функций.– М.: Наука, 1970. 592 с.

2. Valiron G. Sur les valeurs déficientes des fonctions méromorphes d'ordre nul // C.R. Acad. Sci. Paris. 1950. V.230. N.1. P.40–42.

3. Anderson J. Asymptotic values of meromorphic functions of smooth grouth // Glasgow Math. J. 1979. V.20, N.2. P.155–162.

4. Бiлобрам Л.В., Заболоцький М.В. Достатнi умови повiльного зростання опуклих функцiй // Вiсник Львiв. ун-ту. 1988. Вип. 30. С.25–27

5. Hayman W. On Iversen's theorem for meromorphic functions with few poles // Acta Math. 1978. V.141, N.1–2. P.115–145 Department of Mechanics and Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine

	Equivalence of two classes of meromorphic functions (in Ukrainian)
Author	M. Zabolotskyy Department of Mechanics and Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine
Abstract	It is shown that for every meromorphic in $\Bbb C$ function $f$ with $T(2r,f)\sim T(r,f)$, $r\to\infty$ we have $$ r\smallint_r^{+\infty}\frac{n(t,a,f)}{t^2}dt=o(T(r,f)),\; r\to\infty. $$ for each $a \in \hat {\Bbb C}$. Conversely, if the last condition holds for two values $a,b\in \hat {\Bbb C}$ and $f$ is of genus zero, then $T(2r,f)\sim T(r,f)$, $r\to\infty$.
Keywords	meromorphic function, complex plane, genus zero
DOI	doi:10.30970/ms.2.1.41-45
Reference	1. Гольдберг А.А., Островский И.В. Распределение значений мероморфных функций.– М.: Наука, 1970. 592 с. 2. Valiron G. Sur les valeurs déficientes des fonctions méromorphes d'ordre nul // C.R. Acad. Sci. Paris. 1950. V.230. N.1. P.40–42. 3. Anderson J. Asymptotic values of meromorphic functions of smooth grouth // Glasgow Math. J. 1979. V.20, N.2. P.155–162. 4. Бiлобрам Л.В., Заболоцький М.В. Достатнi умови повiльного зростання опуклих функцiй // Вiсник Львiв. ун-ту. 1988. Вип. 30. С.25–27 5. Hayman W. On Iversen's theorem for meromorphic functions with few poles // Acta Math. 1978. V.141, N.1–2. P.115–145 Department of Mechanics and Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine
Pages	41-45
Volume	2
Issue	1
Year	1993
Journal	Matematychni Studii
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