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Zeros of higher derivatives of meromorphic functions in the complex plane
Author(s) -
Yamanoi Katsutoshi
Publication year - 2013
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pds051
Subject(s) - meromorphic function , complex plane , conjecture , mathematics , plane (geometry) , pure mathematics , derivative (finance) , function (biology) , mathematical analysis , geometry , evolutionary biology , financial economics , economics , biology
We prove the Gol’dberg conjecture, which states that the frequency of distinct poles of a meromorphic function f in the complex plane is governed by the frequency of zeros of the second derivative f ″. As a consequence, we prove Mues’ conjecture concerning the defect relation for the derivatives of meromorphic functions in the complex plane.