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Page 79
Walter Kurt Hayman. 4 FURTHER RESULTS ABOUT DEFICIENCIES 4.0 . Introduction In this chapter we consider further the possible deficient values and the values of their deficiencies for functions f ( z ) meromorphic in the plane . This ...
Walter Kurt Hayman. 4 FURTHER RESULTS ABOUT DEFICIENCIES 4.0 . Introduction In this chapter we consider further the possible deficient values and the values of their deficiencies for functions f ( z ) meromorphic in the plane . This ...
Page 124
... deficient values . If p < 1⁄2 , it follows from Theorem 4.11 that such a function cannot have any finite deficient values , but nothing is known in general for p > 1 . In certain special cases we have some information . Thus Edrei and ...
... deficient values . If p < 1⁄2 , it follows from Theorem 4.11 that such a function cannot have any finite deficient values , but nothing is known in general for p > 1 . In certain special cases we have some information . Thus Edrei and ...
Page 184
... deficient values of certain classes of mero- morphic functions ' , Proc . London Math . Soc . 12 ( 1962 ) , 315–44 . EDREI , A. , FUCHS , W. H. J. and HELLERSTEIN , S. [ 1 ] ' Radial distribution and deficiencies of the values of a ...
... deficient values of certain classes of mero- morphic functions ' , Proc . London Math . Soc . 12 ( 1962 ) , 315–44 . EDREI , A. , FUCHS , W. H. J. and HELLERSTEIN , S. [ 1 ] ' Radial distribution and deficiencies of the values of a ...
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