ZHANG Xue-lian. The Deficiency and Nevanlinna Direction of the Meromorphic Functions[J]. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 1999, 8(1): 14-18.
Citation:
ZHANG Xue-lian. The Deficiency and Nevanlinna Direction of the Meromorphic Functions[J].JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 1999, 8(1): 14-18.
ZHANG Xue-lian. The Deficiency and Nevanlinna Direction of the Meromorphic Functions[J]. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 1999, 8(1): 14-18.
Citation:
ZHANG Xue-lian. The Deficiency and Nevanlinna Direction of the Meromorphic Functions[J].JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 1999, 8(1): 14-18.
Aim To study the value distribution of meromorphic functions in angular domains, the deficiency, the deficient value, the Nevanlinna direction and other singular directions. Methods A fundamental inequality of Nevanlinna characteristic functions in the angular domain was used, which is similar with the Nevanlinna secondary fundamental theorem. Results The deficiency and deficient value of meromorphic functions about an angular domain and a direction were defined. The definition of Nevanlinna direction was improved. Conclusion For a family of meromorphic functions, it is proved that the number of deficient values is at most countable and the sum of deficiencies isnt greater than 2. The existence of the Nevanlinna direction is obtained. The existence of Borel and Julia directions and the relation between them are found.
Zhang Xuelian. A fundemental inequality for meromorphic functions in an angular domain and its ap??plication. Acta Mathematica Sinica, New Series, 1994, 10(3) : 308- 314
[2]
Lü Yinian, Zhang Guanghou. On Nevanlinna direction of a meromorphic function. Scientia Sinica( Series A) , 1983, 26( 6) : 607- 617
[3]
Tsuji M. Potential theory in modern function theory . Tokyo: Marazen Co. Ltd. , 1959