The First Fundamental Theorem of Nevanlinna Theory

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.