Skip to main content

Algebroid reduction of Nevanlinna theory

Special Year Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 1277)

Keywords

  • Complex Manifold
  • Holomorphic Section
  • Complex Vector Space
  • Holomorphic Line Bundle
  • Nevanlinna Theory

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Ahlfors. The theory of meromorphic curves. Acta Soc. Sci. Fenn, Nova Ser. A 3 (4) (1941) 171–173.

    MathSciNet  MATH  Google Scholar 

  2. A. Andreotti and W. Stoll. Analytic and algebraic dependence of meromorphic functions. Lecture Notes in Mathematics 234 (1971) 390 pp. Springer-Verlag.

    Google Scholar 

  3. D. Barlet. Espace analytique reduit des cycles analytiques complexes compacts d'un espace analytique complexe de dimension finie. Lecture Notes in Mathematics 482 Fonctions des Plusieurs variables complexes II (1975) 1–158. Springer-Verlag.

    Google Scholar 

  4. H. Cartan. Sur les systèmes de fonctions holomorphes à varieties linéaires et leurs applications. Ann Sci. École Norm. Sup. (3) 45 (1928) 255–346.

    MathSciNet  MATH  Google Scholar 

  5. H. Cartan. Sur les zéros des combinaisons linéaires de p fonctions holomorphes données. Mathematica(Cluj) 7 (1933) 5–31.

    MathSciNet  MATH  Google Scholar 

  6. W. H. Greub: Multilinear Algebra. Die Grundl. d. Math. Wiss. 136 (1967) pp. 224. Springer-Verlag.

    MathSciNet  MATH  Google Scholar 

  7. W.K. Hayman: Meromorphic functions. Oxford Math. Monographs. (1964) pp. 191 Calderon Press, Oxford.

    Google Scholar 

  8. R. Nevanlinna: Le Théorème de Picard-Borel et la Théorie des Fonctions Meromorphes. Gauthiers-Villars, Paris (1929) reprint Chelsea Publ. Co. New York (1974) pp. 171.

    MATH  Google Scholar 

  9. R. Nevanlinna: Eindeutige analytische Funktionen. 2nd ed. Die Grundl. d. Math. Wiss. 46 (1953) pp. 379. Springer-Verlag.

    MATH  Google Scholar 

  10. K. Niino and M. Ozawa: Deficiencies of an entire algebroid function. Kōdai Math. Sem. Report 22 (1970) 98–113.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. J. Noguchi. On the deficiencies and the existence of Picard's exceptional values of entire algebroid functions. Kōdai. Math. Sem. Report 26 (1974) 29–35.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. J. Noguchi: Meromorphic Mappings of a Covering Space over ℂm into a Projective Variety and Defect Relations. Hiroshima Math. J. 6 (1976) 265–280.

    MathSciNet  MATH  Google Scholar 

  13. J. Noguchi: On value distribution of meromorphic mappings of covering spaces over ℂm into algebroid varieties. Preprint pp. 35.

    Google Scholar 

  14. V.P. Petrenko: Growth and distribution of values of algebroid functions. Mat. Zametki 26 (1979) 513–522, 653. Engl. Math. Notes 26 (1979) 3–4, 746–751 (1980).

    MathSciNet  Google Scholar 

  15. R. Remmert: Holomorphe und meromorphe Abbildungen komplexer Räume. Math. Annalen 133 (1957) 328–370.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. R. Remmert and K. Stein: Über die wesentlichen Singularitäten analytischer Mengen. Math. Annalen 126 (1953), 263–306.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. H.L. Selberg: Algebroide Funktionen und Umkehrfunktionen Abelscher Integrale Avh. Norske Vid. Acad. Oslo 8 (1934) 1–72.

    MATH  Google Scholar 

  18. B.V. Shabat: Distribution of Values of Holomorphic Mappings. Transl. of Math. Monog. 61 (1985) pp. 225.

    MathSciNet  Google Scholar 

  19. N. Steinmetz: Eine Verallgemeinerung des zweiten Nevanlinnaschen Hauptsatzes. Preprint 1986 pp. 11.

    Google Scholar 

  20. W. Stoll: Die beiden Hauptsätze der Wertverteilungstheorie bei Funktionen mehrerer komplexer Veränderlichen. I Acta Math. 90 (1953) 1–115 II Acta Math. 92 (1954) 55–169.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. W. Stoll: The multiplicity of a holomorphic map. Invent. Math. 2 (1966) 15–58.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. W. Stoll: Value distribution of holomorphic maps into compact complex manifolds. Lecture Notes in Mathematics 135 (1970) pp. 267. Springer-Verlag.

    MathSciNet  MATH  Google Scholar 

  23. W. Stoll: Deficit and Bezout estimates. Value Distribution Theory. Part B. (ed. by R.O. Kujala and A.L. Vitter III). Pure and Appl. Math. 25 Marcell Dekker, New York, (1973) pp. 271.

    Google Scholar 

  24. W. Stoll: Value distribution on parabolic spaces. Lecture Notes in Mathematics 600 (1977), pp. 216. Springer-Verlag.

    MathSciNet  MATH  Google Scholar 

  25. W. Stoll: The characterization of strictly parabolic manifolds. Annali di Pisa 7 (1980) 87–154.

    MathSciNet  MATH  Google Scholar 

  26. W. Stoll: The characterization of strictly parabolic spaces. Compositio Mathematics 44 (1981) 305–373.

    MathSciNet  MATH  Google Scholar 

  27. W. Stoll: Introduction to value distribution theory of meromorphic maps. Lecture Notes in Mathematics 950 (1982) 210–359. Springer-Verlag.

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. W. Stoll: Value distribution and the lemma of the logarithmic derivative on poly-discs. Internat. J. Math. Sci. 6 (1983) No. 4, 617–669.

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. W. Stoll: The Ahlfors-Weyl theory of meromorphic maps on parabolic manifolds. Lecture Notes in Mathematics 981 (1983) 101–219. Springer-Verlag.

    CrossRef  MathSciNet  MATH  Google Scholar 

  30. W. Stoll: Value distribution theory of meromorphic maps. Aspects of Mathematics E7 1985 pp. 347. Vieweg-Verlag. valeurs

    Google Scholar 

  31. N. Toda: Sur la croissance de fonctions algebroides a valeurs deficientes. Kōdai Math. Sem. Rep. 22 (1970) 324–337.

    CrossRef  MathSciNet  MATH  Google Scholar 

  32. N. Toda: Sur lex combinaisons exceptionnelles de fonctions holomorphes, applications aux fonctions algebroides. Tohoku Math. Journ. 22 (1970) 290–319.

    CrossRef  MathSciNet  MATH  Google Scholar 

  33. N. Toda: Sur le nombre de combinaissons exceptionnelles: applications aux fonctions algebroides. Tôhoku Math. Journ. 22 (1970) 480–491.

    CrossRef  MathSciNet  MATH  Google Scholar 

  34. Ch.Ch. Tung: The first main theorem of value distribution theory on complex spaces. Atti della Acc. Naz. d. Lincei Serie VIII 15 (1979), 93–262.

    MathSciNet  MATH  Google Scholar 

  35. G. Valiron: Sur la derive de fonctions algebroides. Bull Soc. Math. France 59 (1931) 17–29.

    MathSciNet  MATH  Google Scholar 

  36. H. Weyl and J. Weyl. Meromorphic functions and analytic curves. Annals of Math. Studies 12 Princeton Univ. Pr. (1943) pp. 269.

    Google Scholar 

  37. H. Wu: The equidistribution theory of holomorphic curves. Annals of Mathematics Studies 64 Princeton Univ. Pr (1970) pp. 219.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Additional information

Dedicated to Maurice Heins

Rights and permissions

Reprints and Permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Stoll, W. (1987). Algebroid reduction of Nevanlinna theory. In: Berenstein, C.A. (eds) Complex Analysis III. Lecture Notes in Mathematics, vol 1277. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078248

Download citation

  • DOI: https://doi.org/10.1007/BFb0078248

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18355-6

  • Online ISBN: 978-3-540-47893-5

  • eBook Packages: Springer Book Archive