## Meromorphic functions |

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### Contents

THE ELEMENTARY THEORY | 1 |

NEVANLINNAS SECOND FUNDAMENTAL THEOREM | 31 |

DISTRIBUTION OF THE VALUES OF MEROMORPHIC | 55 |

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### Common terms and phrases

Ahlfors Blaschke product bounded characteristic chapter circle completes the proof complex numbers complex plane convex function Corollary corresponding countable set cross-cuts deficient values defined denote differential polynomial disk domain F0 domains G Edrei and Fuchs equation f(z finite linear measure finite number finite order fix-points of exact fn(z function f(z function of order Gol'dberg hence holds hypotheses Iff(z infinite integral function ip(z Jensen's formula Jordan arc Jordan curves least length mean covering number meromorphic function Nevanlinna Nevanlinna theory normal family normal invariant family number of roots obtain Picard's theorem plane points pole of order poles of f(z positive integer positive number proof of Theorem prove Theorem proves Lemma regular relative boundary result Riemann sphere Riemann surface s.a. domain satisfies second fundamental theorem set of finite shows simply connected sufficiently large Suppose that f(z that/(z Theorem 2.1 total number triangle zeros and poles