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

Prool 

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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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