= Nevanlinna second main theorem in the unit disc
{c}
{title2=$(q-2)T(r,f)\le\sum_{j=1}^q\overline N(r;a_j)+O(\log^+T(r,f)+\log(1/(1-r)))$}
For a nonconstant <meromorphic function> on the <unit disc> and $q\ge3$ distinct spherical values, this version of the <Nevanlinna second main theorem> holds outside a set $E$ with $\int_Edr/(1-r)<\infty$, as $r\uparrow1$. The <truncated Nevanlinna counting function> counts distinct preimages rather than <multiplicity>. The boundary-distance error is essential and need not be small relative to the characteristic. It follows from the disk <Nevanlinna logarithmic derivative lemma> and the growth lemma in the variable $\log(1/(1-r))$. The disk error estimate and weighted exceptional-set argument appear in https://mathweb.tifr.res.in/Documents/Publications/Lectures/tifr17.pdf .
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