Existence and some properties of meromorphic functions 
for which Yang Le deficiency relation reaches equality (in Ukrainian)

A.~Gol'dberg

The difference between the deficiency in Yang Le sense and the classical Nevanlinna one consists in that Yang Le deficiency takes into account only $a$-points of order $\le p$, $1\le p\le\infty$. It is shown that Yang Le deficiency relation (1964) cannot be improved. Existence of extremal functions for each $p$ is proved and some their properties are obtained.

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

2. Ян Ле. Кратнi значення мероморфних функцiй та їх комбiнацiй // Шусюе сюебао, Acta math. sinica. 1964. T.14, No 3. C.428–437 (кит.) -3pt

3. (англ. переклад: Yang Le. The multiple values of meromorphic functions and of combinations of functions // Chinese Math. 1964. T.5, No 3. P.460–470 ).

4. Nevanlinna R. Le théorème de Picard-Borel et la théorie des fonctions méromorphes.– Paris: Gauthier-Villars, 1929.– 171 p.

5. Hiong King-lai. Un problème d'unicité relatif aux fonctions méromorphes // Scientia sinica. 1963. V.12, No 6. P.743–750.

6. Виттих Г. Новейшие исследования по однозначным аналитическим функциям. – М.: Физматгиз, 1960.– 320 с.

7. Спрингер Дж. Введение в теорию римановых поверхностей.– М.: ИЛ, 1960.– 344 с.

8. Yi Hong-Xun. On a result of Singh // Bull. Austral. Math. Soc. 1990. V.41. P.417–470. Department of Mechanics and Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine

	Existence and some properties of meromorphic functions for which Yang Le deficiency relation reaches equality (in Ukrainian)
Author	A.~Gol'dberg Department of Mechanics and Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine
Abstract	The difference between the deficiency in Yang Le sense and the classical Nevanlinna one consists in that Yang Le deficiency takes into account only $a$-points of order $\le p$, $1\le p\le\infty$. It is shown that Yang Le deficiency relation (1964) cannot be improved. Existence of extremal functions for each $p$ is proved and some their properties are obtained.
Keywords	Yang Le deficiency, Nevanlinna deficiency, a-points, extremal functions, properties
DOI	doi:10.30970/ms.3.1.53-60
Reference	1. Гольдберг А.А., Островский И.В. Распределение значений мероморфных функций. – М.: Наука, 1970.– 592 с. 2. Ян Ле. Кратнi значення мероморфних функцiй та їх комбiнацiй // Шусюе сюебао, Acta math. sinica. 1964. T.14, No 3. C.428–437 (кит.) -3pt 3. (англ. переклад: Yang Le. The multiple values of meromorphic functions and of combinations of functions // Chinese Math. 1964. T.5, No 3. P.460–470 ). 4. Nevanlinna R. Le théorème de Picard-Borel et la théorie des fonctions méromorphes.– Paris: Gauthier-Villars, 1929.– 171 p. 5. Hiong King-lai. Un problème d'unicité relatif aux fonctions méromorphes // Scientia sinica. 1963. V.12, No 6. P.743–750. 6. Виттих Г. Новейшие исследования по однозначным аналитическим функциям. – М.: Физматгиз, 1960.– 320 с. 7. Спрингер Дж. Введение в теорию римановых поверхностей.– М.: ИЛ, 1960.– 344 с. 8. Yi Hong-Xun. On a result of Singh // Bull. Austral. Math. Soc. 1990. V.41. P.417–470. Department of Mechanics and Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine
Pages	53-60
Volume	3
Issue	1
Year	1994
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Existence and some properties of meromorphic functions for which Yang Le deficiency relation reaches equality (in Ukrainian)