A L Cauchy 1789 1857 G F B

柯西（A. L. Cauchy, 1789 -1857）

黎曼（G. F. B. Riemann, 1826 -1866）

外尔斯特拉斯（K. T. W. Weierstrass, 1815 -1897）

Liouville 定理 Picard 定理 Borel 定理

皮卡（C. É. Picard, 1856 -1941）

波莱尔(F. É. J. É. Borel, 18711956)

Picard, Borel, Poincaré, Hadamard, Valiron, Montel, Julia, Denjoy Milloux, Littlewood Nevanlinna, Ahlfors

奈望林纳（R. Nevanlinna, 1895 -1980）

早期研究 作: R. Nevanlinna: “ Le théorème de Picard-Borel et la théorie des fonctions méromorphes” G. Valiron: “ Directions de Borel des fonctions méromorphes. ” 1964. Yang L. & Zhang G. H. : 正规族， 中国科学 1965年 9月号上 1964. W. K. Hayman 伦敦会议提出问题 1967 问题集出版 1969 D. Drasin Acta Math. 引用 1975 得到问题集的复印件

A Mathematical Visit to China, May 1976 (Notice AMS, 1977, Vol. 24, No. 2, 110 -113) S. Mac. Lane, W. Feit, J. J. Kohn, H. O. Pollak, H. H. Wu E. H. Brown, G. F. Carrier, J. B. Keller, V. L. Klee Even under these restricted circumstances, much of the research in pure mathematics is first-rate, and some of the recent results are important contributions. Particular mention should be made of the Goldbach conjecture and Nevanlinna theory.

Analysis. A very small number of mathematicians are doing research in analysis. Some of the original work is really outstanding, and it is even more impressive when one takes into account the isolation in which it has taken place. In particular, work on analytic number theory and meromorphic functions is excellent. Complex Analysis. The most noteworthy contribution of Chinese mathematics in complex analysis lies in classical Nevanlinna theory, in work done by Yang Le and Chang Guang-hou of the Mathematics Institute of Peking. This area, which requires formidable analytic techniques, has been ploughed over carefully by many specialists all over the world for fifty years. Yang and Chang found something both new and deep to say about Borel directions and the number of deficient values of meromorphic functions. For instance, Theorem ……

Joel L. Schiff, Normal Families, Springer-Verlag, 1993, 236 pages.

Yang L. Sur les valeurs quasi-exceptionnèlles des functions holomorphes, Sci. Sinica 13(1964), 879 -885 [66] Meromorphic functions and their derivatives, J. London Math. Soc. , (2)25(1982), 288 -296. [144] Normal families and differential polynomials, Sci. Sinica, Ser. A, 26(1983), 673 -686. [159] A general criterion for normality, Acta Math. Sinica (New Series) 1(1985), 181 -193. [151] Normal families and fix-points of meromorphic functions, Indiana Univ. Math. J. ，35(1986), 179 -191. [150] Normality for families of meromorphic functions, Sci. Sinica, Ser. A 29 (1986), 1263 -1274. [150]

Yang L. , Chang. K. Recherches sur la normalité des familes des functions analytiquès a des valeurs multiples, I. Un noveau critère et quelques applications, Sci. Sinica 14(1965), 1258 -1271, [58，65，66，132] II. Généralizations, Sci. Sinica 15 (1966), 433 -453. [105. 150] Normality for families of meromorphic functions, Sci. Sinica, Ser. A 29 (1986), 1263 -1274. [150] PP. 144 - 150

Encyclopaedia of Mathematical Sciences A. A. Gonchar, V. P. Havin, N. K. Nikolski(Eds): Complex Analysis, Springer-Verlag, 1997, 261 pages. (Russian edition, 1991)

Author Index Yang Lo, 103, 104, 116, 117, 121, 123, 124, 176, 193

By J(f) and B(f) we shall denote the set of Julia and Borel directions, respectively, of a function f. Yang Lo and Zhang Guanghou (1975, 1976) described the set B(f) completely. Let 0＜ λ ＜+∞ and let E be a non-empty closed set on a unit circumference. Then there exists a meromorphic function f of order λ , for which Yang Lo and Chang Guanghou (1976) discovered an interesting relation between the number of deficient values and the number of Borel’s directions: card , where the equality may be achieved if.