# On the characteristic of functions meromorphic in the unit disk and of their integrals

```@article{Hayman1964OnTC,
title={On the characteristic of functions meromorphic in the unit disk and of their integrals},
author={Walter Kurt Hayman},
journal={Acta Mathematica},
year={1964},
volume={112},
pages={181-214}
}```
• W. Hayman
• Published 1 December 1964
• Philosophy, Mathematics
• Acta Mathematica
n(r, F) as the number of poles in ]z] d r and = f r n(t, F) dt N(r, F) J0 \$ Then T(r, F) = re(r, F) + N(r, F) is called the Nevanlinna characteristic function of F(z). The function T(r, F ) i s convex increasing function of log r, so tha t T(1, F) = lim T(r, F) r--~l always exists as a finite or infinite limit. I f T(1, F) is finite we say tha t F(z) has bounded characteristic in ]z] < 1. Examples show tha t F(z) m a y have bounded characteristic in ]z] < 1, even i f / (z) does not.(1) We may…
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