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Science China Mathematics

, Volume 53, Issue 3, pp 513–522 | Cite as

Value distribution theory and the research of Yang Lo

  • W. K. Hayman
  • ShengJian Wu
Reviews

Abstract

Value distribution theory is concerned with the position and frequency of solutions of the equation f(z) = a. Here f may be entire, i.e. an everywhere convergent power series or meromorphic, i.e. the ratio of two such series, or a function in some other domains, such as an angle or a disk.

Yang Lo’s significant contributions to this area will be highlighted. Some of his important contributions to normal families will also be described.

Keywords

meromorphic function value distribution deficient value angular distribution 

MSC(2000)

30D10 30D20 

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List of Publications (Yang Lo) I. Papers

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    Yang L, Zhang G H. Sur la distribution des directions de Borel des functions méromorphes. Scientia Sinica, 1973, 16: 465–482zbMATHMathSciNetGoogle Scholar
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    Yang L, Zhang G H. Deficient values and Borel directions of meromorphic functions (in Chinese). Bull Science, 1974, 19: 469–470Google Scholar
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    Yang L, Zhang G H. Tangential cluster sets and boundary properties of meromorphic functions (in Chinese). Acta Math Sinica, 1975, 18: 136–148zbMATHGoogle Scholar
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    Yang L, Zhang G H. Deficient values of entire functions (in Chinese). Acta Math Sinica, 1975, 18: 35–53zbMATHMathSciNetGoogle Scholar
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    Yang L, Zhang G H. Recherches sur le nombre des valeurs déficientes et le nombre des directions de Borel des fonctions méromorphes. Scientia Sinica, 1975, 18: 23–37Google Scholar
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    Yang L, Zhang G H. Distribution of Borel directions of entire functions (in Chinese). Acta Math Sinica, 1976, 19: 157–168zbMATHMathSciNetGoogle Scholar
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    Yang L, Zhang G H. Sur la construction des fonctions méromorphes ayant des directions singulières données. Scientia Sinica, 1976, 19: 445–459zbMATHMathSciNetGoogle Scholar
  13. 31.
    Yang L, Zhang G H. Development of value distribution theory of meromorphic functions (in Chinese). Bull Science, 1977, 22: 375–380zbMATHGoogle Scholar
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    Yang L, Zhang G H. Deficient values of extremal entire functions. Scientia Sinica, 1977, 20: 421–435zbMATHMathSciNetGoogle Scholar
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    Ynag L. Borel directions of meromorphic functions in an angle (in Chinese). Scientia Sinica, 1979, Special Issue (I): 149–164Google Scholar
  16. 34.
    Yang L, Zhang G H. Deficient values and asymptotic values of entire functions. Scientia Sinica, 1979, Special Issue (II): 190–203Google Scholar
  17. 35.
    Yang L. Common Borel directions of a meromorphic function and its derivatives. Scientia Sinica, 1979, Special Issue (II): 91–104Google Scholar
  18. 36.
    Yang L, Hayman W K. Value distribution of holomorphic functions in an angle (in Chinese). Bull Science, 1980, 25: 385–388MathSciNetGoogle Scholar
  19. 37.
    Yang L. Angular distribution and multiple values between entire functions and their derivatives. Scientia Sinica, 1980, 23: 16–39zbMATHMathSciNetGoogle Scholar
  20. 38.
    Drasin D, Weitsman A, Yang L, Zhang G H. Deficient values of entire functions and their derivatives. Proc Amer Math Soc, 1981, 82: 607–612zbMATHCrossRefMathSciNetGoogle Scholar
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    Yang L. Deficient functions of meromorphic functions. Scientia Sinica, 1981, 24: 1179–1189zbMATHMathSciNetGoogle Scholar
  22. 40.
    Yang L, Zhang G H. Deficient values of meromorphic functions and their derivatives (in Chinese). Acta Math Sinica, 1982, 25: 617–625zbMATHMathSciNetGoogle Scholar
  23. 41.
    Yang L. Value distribution of meromorphic functions and their derivatives. Scientia Sinica Ser A, 1982, 25: 572–582zbMATHGoogle Scholar
  24. 42.
    Yang L, Zhang G H. A general theorem on the number of deficient values of entire functions (in Chinese). Acta Math Sinica, 1982, 25: 244–247zbMATHMathSciNetGoogle Scholar
  25. 43.
    Yang L, Zhang G H. Distribution of zeros and poles of meromorphic functions and their filling disks. Scientia Sinica Ser A, 1982, 25: 371–383Google Scholar
  26. 44.
    Hayman W K, Yang L. Growth and values of functions regular in an angle. Proc London Math Soc, 1982, 44: 193–214zbMATHCrossRefMathSciNetGoogle Scholar
  27. 45.
    Yang L. Meromorphic functions and their derivatives. J London Math Soc, 1982, 25: 288–296zbMATHCrossRefMathSciNetGoogle Scholar
  28. 46.
    Yang L. Bloch principle and related topics (in Chinese). J East China Normal Univ, 1983, 1–6Google Scholar
  29. 47.
    Yang L. A fundamental inequality and its applications. Chin Ann Math Ser B, 1983, 4: 339–346Google Scholar
  30. 48.
    Yang L. Normal families and differential polynomials. Scientia Sinica Ser A, 1983, 26: 673–686zbMATHGoogle Scholar
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    Lang R L, Yang L. BMO functions in spaces of homogeneous type. Scientia Sinica Ser A, 1984, 27: 695–708Google Scholar
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    Yang L. Quasi-deficient values of meromorphic functions (in Chinese). Acta Math Sinica, 1984, 27: 249–256zbMATHMathSciNetGoogle Scholar
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    Yang L, Zhang Q D. New singular directions of meromorphic functions. Scientia Sinica Ser A, 1984, 27: 352–366zbMATHGoogle Scholar
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    Yang L, Chuang C T. Distribution of the values of meromorphic functions. Contemp Math, 1985, 48: 21–63MathSciNetGoogle Scholar
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    Yang L, Zhang Q D. Normality for families of meromorphic functions. Scientia Sinica Ser A, 1986, 29: 1263–1274zbMATHGoogle Scholar
  37. 55.
    Yang L. Angular distribution of meromorphic functions and their derivatives (in Chinese). Acta Math Sinica, 1986, 29: 355–361zbMATHMathSciNetGoogle Scholar
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    Yang L. Some results on value distribution theory of entire and meromorphic functions. Adv Sci China Math, 1986, 1: 199–223Google Scholar
  39. 57.
    Yang L. Normal families and fix-points of meromorphic functions. Indiana Univ Math J, 1986, 35: 179–191zbMATHCrossRefMathSciNetGoogle Scholar
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    Yang L. On the deficient values and angular distribution (in Chinese). Bull Science, 1987, 32: 885–888Google Scholar
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    Yang L. Angular distribution of meromorphic functions in the unit disk. In: Complex Analysis. Basel: Birkhäuser-Verlag, 1988, 239–245Google Scholar
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    Yang L. Deficient values and angular distribution of entire functions. Trans Amer Math Soc, 1988, 308: 583–601zbMATHCrossRefMathSciNetGoogle Scholar
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    Yang L. Growth and angular distribution of entire functions. Complex Var, 1989, 13: 155–160zbMATHGoogle Scholar
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    Yang L. Precise estimate of total deficiency for derivatives of meromorphic functions (in Chinese). Bull Science, 1990, 35: 1208–1210Google Scholar
  45. 63.
    Yang L. Results and problems in the value distribution theory of meromorphic functions (in Chinese). In: Proceedings of Conference in Memory of T.H. Min. Jinan: Shandong University Press, 1990, 49–55Google Scholar
  46. 64.
    Yang L. Precise estimate of total deficiency of meromorphic derivatives. J Anal Math, 1990, 55: 287–296zbMATHCrossRefGoogle Scholar
  47. 65.
    Yang L. Deficient values and deficient functions of meromorphic functions. In: International Symposium in Memory of Hua Loo Keng. Berlin-Beijing: Springer-Verlag & Science Press, 1991, 313–321Google Scholar
  48. 66.
    Yang L. On the total deficiency of meromorphic functions concerning their derivatives (in Chinese). Bull Science, 1991, 36: 1761–1763Google Scholar
  49. 67.
    Yang L. Precise fundamental inequalities and sum of deficiencies. Sci China Ser A, 1991, 34: 157–165zbMATHMathSciNetGoogle Scholar
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    Yang L. Some recent results and problems in the theory of value distribution. In: Proceedings of Symposium on Value Distribution Theory in Several Complex Variables. Notre Dame: University of Notre Dame Press, 1992, 157–171Google Scholar
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    Yang L. Total deficiency of meromorphic functions and their derivatives. In: Proceedings of the Asian Math Conference. Singapore: World Scitific Publication Company, 1992, 519-523Google Scholar
  52. 70.
    Yang L, Wang Y F. Drasin’s problem and Mues’ conjecture. Sci China Ser A, 1992, 35: 1180–1190zbMATHMathSciNetGoogle Scholar
  53. 71.
    Yang L, Wang Y F, Yang C C. On the zeros of (f k)(n) f − a (in Chinese). Bull Science, 1993, 38: 2209–2212Google Scholar
  54. 72.
    Yang L. Several results and problems in the theory of value distribution. SEA Bull Math, 1993, Special Issue: 175–183Google Scholar
  55. 73.
    Yang L. Angular distribution of values of ff′. Sci China Ser A, 1994, 27: 284–294Google Scholar
  56. 74.
    Yang L. Kinglai Hiong: A brief outline of his life and works. In: Proceedings of the International Conference on Complex Ananlysis. Somerville, MA: International Press, 1994, 3–7Google Scholar
  57. 75.
    Sun D C, Yang L. Value distribution of quasiconformal mappings. Complex Var, 1997, 34: 219–229zbMATHMathSciNetGoogle Scholar
  58. 76.
    Yang L. History and development of value distribution theory in China. Complex Var Theory Appl, 1998, 37: 507–523zbMATHGoogle Scholar
  59. 77.
    Yang L. Some results and problems in the theory of value distribution. In: Proceedings of the Second Asian Math Conference. Singapore: World Scientific Publication Company, 1998, 85–93Google Scholar
  60. 78.
    Sun D C, Yang L. Quasi-rational dynamics (in Chinese). Bull Science, 1999, 44: 1481–1483Google Scholar
  61. 79.
    Sun D C, Yang L. Quasirational dynamical system (in Chinese). Chin Ann Math Ser A, 1999, 20: 673–684zbMATHMathSciNetGoogle Scholar
  62. 80.
    Yang L. In memory of Professor C.T. Chuang. In: Proceedings of the Eighth International Colloquium on Finite or Infinite Dimensional Complex Analysis. Jinan: Shangdong Sci & Tech Press, 2001, 1–4Google Scholar
  63. 81.
    Sun D C, Yang L. Iteration of quasi-rational mapping. Progr Natur Sci (English Ed), 2001, 11: 16–25MathSciNetGoogle Scholar
  64. 82.
    Sun D C, Yang L. Normal family of algebroidal functions. Sci China Ser A, 2001, 44: 1271–1277zbMATHCrossRefMathSciNetGoogle Scholar
  65. 83.
    Sun D C, Yang L. Normal family of quasimeromorphic mappings. Sci China Ser A, 2003, 46: 440–449CrossRefMathSciNetGoogle Scholar

II. Monographes

  1. 84.
    Yang L. Theory of Value-Distribution and its New Development (in Chinese). Beijing: Science Press, 1982Google Scholar
  2. 85.
    Yang L. Value Distribution Theory. Berlin: Springer-Verlag, 1993zbMATHGoogle Scholar

III. Proceedings

  1. 86.
    International Smyposium in Memory of Hua Loo Keng, vol. I, Number Theory. Berlin: Springer-Verlag, 1991 (edited with Sheng Gong, Qi-Keng Lu and Yuan Wang)Google Scholar
  2. 87.
    International Smyposium in Memory of Hua Loo Keng, vol. II, Analysis. Berlin: Springer-Verlag, 1991 (edited with Sheng Gong, Qi-Keng Lu and Yuan Wang)Google Scholar
  3. 88.
    Proceedings of Asian Mathematical Conference 1990. Singapore: World Scientific Publication Company, 1992 (edited with Zhong Li, K.P. Shum and C.C. Yang)Google Scholar
  4. 89.
    Lectures Notes in Contemporary Mathematics, vol. 2. Beijing-New York: Science Press, 1992 (edited with Bingren Li and Shixue Zhu)Google Scholar
  5. 90.
    Proceedings of International Conference on Complex Analysis, Nankai Institute of Mathematics, 1992. Somerville: International Press, 1994 (edited with Zhong Li, Fuyao Ren and Shunyan Zhang)Google Scholar
  6. 91.
    Sixty years of Chinese Mathematical Society (in Chinese). Changsha: Hunan Education Press, 1996Google Scholar
  7. 92.
    First International Congress of Chinese Mathematicians, Proceedings of ICCM 98. Providence, RI-Somerville, MA: American Mathematical Society & International Press (edited with Shing-Tong Yau)Google Scholar
  8. 93.
    Proceedings of the Eighth International Colloquium on Finite or Infinite Dimensional Complex Analysis. Jinan: Shandong Sci & Tech Press, 2001 (edited with Hong-Xun Yi)Google Scholar
  9. 94.
    Proceedings of Third Asian Mathematics Conference 2000. Singapore: World Scitific Publication Company, 2002 (edited with T. Sunada & P.W. Sy)Google Scholar
  10. 95.
    Second International Congress of Chinese Mathematicians, Proceedings of ICCM 2001. Somerville, MA: International Press, 2004 (edited with Chang-Shou Lin & Shing-Tong Yau)Google Scholar
  11. 96.
    Proceedings of the 4th International Congress of Chinese Mathematicians, vols. I, II, III. Beijing: Higher Education Press, 2007 (edited with Lizhen Ji, Kefeng Liu and Shing-Tong Yau)Google Scholar
  12. 97.
    Proceedings of the 13th International Conference on Finite and Infinite Dimensional Complex Analysis and Applications. Singapore: World Scitific Publication Company, 2006 (edited with Yuefei Wang, Shengjian Wu and Hasi Wulan)Google Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Mathematics, Imperial College LondonSouth Kensington CampusLondonUK
  2. 2.LMAM School of Mathematical SciencesPeking UniversityBeijingChina

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