Meromorphic Functions |
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Page 140
... relative boundary of the map and S1 ( B ) the covering number of this map over the boundary arc ẞn for n = 1 to q . Then Theorem 5.2 yields | S1 ( B , ) — S1 < hL1 ( n = 1 to q ) . ( 5.10 ) We apply ( 5.10 ) in particular to each domain ...
... relative boundary of the map and S1 ( B ) the covering number of this map over the boundary arc ẞn for n = 1 to q . Then Theorem 5.2 yields | S1 ( B , ) — S1 < hL1 ( n = 1 to q ) . ( 5.10 ) We apply ( 5.10 ) in particular to each domain ...
Page 141
... boundary of Au . Using ( 5.10 ) we deduce , if S is again the mean covering number of the map of Aμ , and L , the length of the relative boundary of the map , that Adding for μ = v + 1 to 7 , we deduce Sp μ Eμ ( oμ ) + hLμ · μ S ( 2 ) ...
... boundary of Au . Using ( 5.10 ) we deduce , if S is again the mean covering number of the map of Aμ , and L , the length of the relative boundary of the map , that Adding for μ = v + 1 to 7 , we deduce Sp μ Eμ ( oμ ) + hLμ · μ S ( 2 ) ...
Page 146
... relative boundary of the map of [ z ] < r into the Riemann w - sphere . Consider now a domain G ' . It is divided into islands Gi and domains G by Jordan curves in the interior of G ' . Only one such domain Ğ meets the boundary of G ...
... relative boundary of the map of [ z ] < r into the Riemann w - sphere . Consider now a domain G ' . It is divided into islands Gi and domains G by Jordan curves in the interior of G ' . Only one such domain Ğ meets the boundary of G ...
Contents
THE ELEMENTARY THEORY | 1 |
NEVANLINNAS SECOND FUNDAMENTAL THEOREM | 31 |
DISTRIBUTION OF THE VALUES OF MEROMORPHIC | 55 |
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a₁ Ahlfors arcs assume b₁ Blaschke product bounded characteristic C₁ chapter circle completes the proof complex numbers convex function COROLLARY corresponding countable set cross-cuts deficient values defined denote differential polynomial disk domains G Edrei equation f(z finite linear measure finite number finite order fix-points of exact function of order Gol'dberg h₁ hence holds hypotheses infinite integer integral function islands Jensen's formula Jordan arc Jordan curves length log+ mean covering number meromorphic function multiplicity Nevanlinna normal invariant family obtain Picard's theorem plane points pole of order poles of f(z polynomial positive integer positive number proof of Theorem prove Theorem proves Lemma r₁ reio relative boundary result Riemann sphere Riemann surface s.a. domain satisfies second fundamental theorem sequence shows simply connected sufficiently large Suppose that f(z Theorem 2.1 triangle uniformly w₁ zeros and poles πρ