Schlicht regions for entire and meromorphic functions | Zendy

Mario Bonk | Zendy; Alexandre Erëmenko | Zendy

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Schlicht regions for entire and meromorphic functions

Author(s) -

Mario Bonk,

Alexandre Erëmenko

Publication year - 1999

Publication title -

journal d analyse mathématique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.189

H-Index - 53

eISSN - 1565-8538

pISSN - 0021-7670

DOI - 10.1007/bf02791258

Subject(s) - meromorphic function , mathematics , genus , normality , metric (unit) , class (philosophy) , elliptic function , rational function , pure mathematics , infinity , function (biology) , algebraic number , degree (music) , mathematical analysis , computer science , statistics , economics , biology , operations management , artificial intelligence , evolutionary biology , botany , physics , acoustics

Let f:C →C be a meromorpMc function. We study the size of the maximal disc inC, with respect to the spherical metric, in which a single-valued branch of f-1 exists. This problem is related to normality and type criteria. Best possible lower estimates of the size of such discs are obtained for entire functions and a class of meromorphic functions containing all elliptic functions. An estimate for the class of rational functions is also given which is best possible for rational functions of degree 7. For algebraic functions of given genus we obtain an estimate which is precise for genera 2 and 5 and asymptotically best possible when the genus tends to infinity.

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