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The Theorem of Tumura‐Clunie for Meromorphic Functions
Author(s) -
Mues E.,
Steinmetz N.
Publication year - 1981
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-23.1.113
Subject(s) - meromorphic function , mathematics , algebra over a field , physics , library science , computer science , pure mathematics
.ThenThis resul wat s first stated b y Tumura [5]. His proof however, wa, s incomplete.The assumption of Theores Am can b weakenee (seed , exampl for e Hayman[3; p. 69]), but it is always required tha tht e logarithmic derivative ¥'/¥ is a functionof small growth / compare in sens thede wit defineh d above. SinceT{r, V/V) ^ N(r, ¥ N(r,f)) ^ + S(r,f), th logarithmie c derivativ no havte doee sthis propert iyf / is arbitrar an y meromorphic function For example . i,ff(z) = tan anz d V 1 + / =