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Value distribution theory and the research of Yang Lo. (English) Zbl 1195.30005
This paper describes the important contributions due to Yang Lo in the field of value distribution theory of meromorphic functions over four decades. After a short introduction to the basic notions and key results of Nevanlinna theory, the main achievements due to Yang Lo are described in three sections: (1) Concerning angular distributions of meromorphic functions, his co-operation with Zhang Guanghou resulted in a number of remarkable results, including the Yang–Zhang theorem, that describes a close relation between the number of deficient values and the number of Borel directions. (2) As to the deficient values of meromorphic functions, the Yang Lo relation gives an extension involving multiplicities to the usual deficiency relation. (3) Finally, Yang Lo’s results related to the Bloch principle for normal families are shortly presented. A complete list of publications by Yang Lo finishes the paper.
MSC:
30-03Historical (functions of one complex variable)
30D10Representations of entire functions by series and integrals
30D20General theory of entire functions
References:
[1]Borel E. Sur les zéros des fonctions entières. Acta Math, 1897, 20: 357–396 · Zbl 02673501 · doi:10.1007/BF02418037
[2]Drasin D. Normal families and the Nevanlinna theory. Acta Math, 1969, 122: 231–363 · Zbl 0176.02802 · doi:10.1007/BF02392012
[3]Drasin D. A meromorphic function with assigned Nevanlinna deficiencies. In: Proceedings of the Sysposium on Complex Analysis. LMS Lecture Notes Series No. 12, 1974, 312–342
[4]Drasin D, Weitsman A. On the Julia directions and Borel directions of entire functions. Proc London Math Soc, 1976, 32: 199–212 · Zbl 0318.30030 · doi:10.1112/plms/s3-32.2.199
[5]Gol’dberg A A. Existence and some properties of meromorphic functions for which the Yang Le deficiency relation reaches equality. Mat Stud, 1994, 3: 53–60
[6]Hadamard J. Essai sur l’étude des fonctions données par leur développement de Taylor. J Math Pure Appl, 1892, 8: 101–186
[7]Hayman W K. Picard values of meromorphic functions and their derivatives. Ann of Math, 1959, 70: 9–52 · Zbl 0088.28505 · doi:10.2307/1969890
[8]Hayman W K. Research Problems in Function Theory. London: Athlone Press, 1967
[9]Jensen J L W V. Sur un nouvel et important théorème de la théorie des fonctions. Acta Math, 1899, 22: 359–364 · Zbl 02668299 · doi:10.1007/BF02417878
[10]Milloux H. Les Fonctions Méromorphes et Leurs Derivées. Paris: Hermann, 1940
[11]Montel P. Leçons sur les Familles Normales de Fonctions Analytiques et Leurs Applications. Paris: Gauthier-Villars, 1927
[12]Mues E. Über eine Defekt und Verzweigungsrelation für die Ableitung Meromorpher Funktionen. Manuscripta Math, 1971, 5: 275–2 · Zbl 0225.30031 · doi:10.1007/BF01443259
[13]Nevanlinna R. Le Théorème de Picard-Borel et la Théorie des Fonctions Méromorphes. Paris: Gauthier-Villars, 1929
[14]Oshkin I B. On a test of the normality of holomorphic functions. Uspehi Mat Nauk, 1982, 37: 221–222 (Russian Math Surveys, 1982, 37: 237–238)
[15]Pang X, Zalcman L. Normal families and shared values. Bull London Math Soc, 2000, 32: 325–331 · Zbl 1030.30031 · doi:10.1112/S002460939900644X
[16]Picard É. Sur une propriété des fonctions entières. C R Math Acad Sci Paris, 1897, 88: 1024–1027
[17]Zalcman L. A heuristic principle in complex function theory. Amer Math Monthly, 1975, 82: 813–817 · Zbl 0315.30036 · doi:10.2307/2319796
[18]Zhang G H. On the research of common Borel directions of a meromorphic function with its derivatives. Acta Math Sinica, 1977, 20: 237–247