Nevanlinna second main theorem (source code)

= Nevanlinna second main theorem
{c}
{title2=$(q-2)T_f\le\sum_{j=1}^q\overline N(r;a_j)+S_f$}

= Nevanlinna second fundamental theorem
{c}
{synonym}

For distinct fixed target values and a nonconstant <meromorphic function>, the truncated second main theorem has the displayed form, with $S_f=O(\log^+T_f+\log r)$ outside a set of finite linear measure. The <truncated Nevanlinna counting function> retains only one unit at each preimage. For finite-order functions the error is $O(\log r)$; for transcendental functions it is $o(T_f)$ along the nonexceptional radii.