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The First Fundamental Theorem of Nevanlinna Theory

  • Lee A. Rubel
  • James E. Colliander
Part of the Universitext book series (UTX)

Abstract

Rewriting Jensen’s Theorem, we get
$$ \frac{1}{{2\pi }}\int_{{ - \pi }}^{\pi } {\log |f(r{{e}^{{i\theta }}})|} \;d\theta = \log |{{a}_{k}}| + N\left( {r,\frac{1}{f}} \right) - N(r,f), $$
(4.1)
where N is a kind of average number of poles of f.

Keywords

Meromorphic Function Bounded Function Fundamental Theorem Simple Property Laurent Expansion 
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 1996

Authors and Affiliations

  • Lee A. Rubel
    • 1
  • James E. Colliander
    • 1
  1. 1.Department of MathematicsUniversity of Illinois, Urbana-ChampaignUrbanaUSA

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