Nevanlinna logarithmic derivative lemma (source code)

= Nevanlinna logarithmic derivative lemma
{c}
{title2=$m(r,f'/f)=O(\log^+T_f(r)+\log r)$}

For a nonconstant <meromorphic function> on the plane, the displayed estimate holds outside an exceptional set of radii of finite linear measure, for large $r$. The <logarithmic derivative> has only simple principal parts at zeros and <poles>; <Poisson-Jensen formula> estimates and control of increasing auxiliary growth functions produce the logarithmic error. It supplies the error term in the <Nevanlinna second main theorem>.