Growth of functions in cercles de remplissage

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dc.contributorVirginia Techen
dc.contributor.authorFenton, P. C.en
dc.contributor.authorRossi, John F.en
dc.contributor.departmentMathematicsen
dc.date.accessed2014-07-15en
dc.date.accessioned2014-07-21T15:49:40Zen
dc.date.available2014-07-21T15:49:40Zen
dc.date.issued2002-02en
dc.description.abstractSuppose that f is meromorphic in the plane, and that there is a sequence z(n) --> infinity and a sequence of positive numbers epsilon(n) --> 0, such that epsilon(n)\z(n)f(#)(z(n))/log\z(n)\ --> infinity. It is shown that if f is analytic and non-zero in the closed discs Delta(n) = {z : \z - z(n)\ less than or equal to epsilon(n)\z(n)\}, n = 1, 2, 3,..., then, given any positive integer K, there are arbitrarily large values of n and there is a point z in Delta(n) such that \f(z)\ > \z\(K). Examples are given to show that the hypotheses cannot be relaxed.en
dc.identifier.citationFenton, P. C.; Rossi, J., "Growth of functions in cercles de remplissage," J. Austral. Math. Soc. 72 (2002), 131-136. DOI: 10.1017/S1446788700003645en
dc.identifier.doihttps://doi.org/10.1017/S1446788700003645en
dc.identifier.issn1446-7887en
dc.identifier.urihttp://hdl.handle.net/10919/49641en
dc.identifier.urlhttp://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=4831012&fulltextType=RA&fileId=S1446788700003645en
dc.language.isoen_USen
dc.publisherCambridge University Pressen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectmathematicsen
dc.titleGrowth of functions in cercles de remplissageen
dc.title.serialJournal of the Australian Mathematical Societyen
dc.typeArticle - Refereeden

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