{"title":"ON BOREL DIRECTION CONCERNING SMALL FUNCTIONS","authors":"T. Chern","doi":"10.5556/J.TKJM.29.1998.4289","DOIUrl":null,"url":null,"abstract":"Let J be a function meromorphic in the finite complex plane C. We donate by T(r, J)(To(r, !)) the Nevanlinna(Ahlfors-Shmizu) characteristic function of J. A mero morphic function a(z) (including the case f(z) == c where c in Cu {oo}) is called small with respect to f if T(r, a(z)) = o(T(r, J)) as r -, +oo. \\Ve let n(兀 <p, a, J = a(z)) be the number of roots (multiple roots being counted with their multiplicities) of the equation j(z) = a(z) for z in the angular domain D(r,cp,a) = {z: largz 列< c..t, lzl < r} where 0 :::; cp < 21r, a > 0. This paper deals with the existence of the Borel directions concerning small functions for mermorphic functions of finite positive order. Using Tsuji's method, we shall mainly prove Theorem 1 stated in the abstract. Theorem~extends a result of Chuang [2, p.127, Corollary 5.3], there a(z} are restricte<l over all extended complex numbm·s. Chuang's method rs different from ours and is區ed on the existence of a sequence of filling disk with their roots in the works of Milloux [3] and Valiron [7].","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tamkang Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5556/J.TKJM.29.1998.4289","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Let J be a function meromorphic in the finite complex plane C. We donate by T(r, J)(To(r, !)) the Nevanlinna(Ahlfors-Shmizu) characteristic function of J. A mero morphic function a(z) (including the case f(z) == c where c in Cu {oo}) is called small with respect to f if T(r, a(z)) = o(T(r, J)) as r -, +oo. \Ve let n(兀 0. This paper deals with the existence of the Borel directions concerning small functions for mermorphic functions of finite positive order. Using Tsuji's method, we shall mainly prove Theorem 1 stated in the abstract. Theorem~extends a result of Chuang [2, p.127, Corollary 5.3], there a(z} are restricte
期刊介绍：
To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
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