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The Theorems of Bloch, Picard, and Schottky

  • Reinhold Remmert
Part of the Graduate Texts in Mathematics book series (GTM, volume 172)

Abstract

The sine function assumes every complex number as a value; the exponential function omits only the value O. These examples are significant for the value behavior of entire functions. A famous theorem of E. Picard says that every nonconstant entire function omits at most one value. This so-called little Picard theorem is an astonishing generalization of the theorems of Liouville and Casorati-Weierstrass.

Keywords

Entire Function Sharpened Form Bloch Constant Nonconstant Entire Function Nonconstant Polynomial 
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.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Reinhold Remmert
    • 1
  1. 1.Mathematisches InstitutWestfälische Wilhelms—Universität MünsterMünsterGermany

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