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Uniqueness Of Entire Functions Concerning Derivatives

Posted on:2003-04-10Degree:MasterType:Thesis
Country:ChinaCandidate:M Z ZhangFull Text:PDF
GTID:2120360062496111Subject:Basic mathematics
Abstract/Summary:PDF Full Text Request
In this paper we study the uniqueness of meromorphic(entire) functions, which is an important subject in complex analysis. Much work was made on this respect.In chapter one we state a few usual notations, definitions and basic results in value distribution theory of meromorphic function.In chapter two, we discuss the uniqueness of entire functions concerning derivatives and mainly prove the following theorem:Let f(z) and g(z) be two nonconstant entire functions, n, k two positive integers with n > Ik + 4. If the zeros of both /(z) and g(z) are of multiplicity at least n, and f(k\z) and g^(z) share 1 CM, then either f(z) = c\ecz, g(z] ?c^e~cz, where c\,c-i and c are three constants satisfying (-1)kc\c2c2k = 1, or f(z) = g(z).
Keywords/Search Tags:Entire function, sharing value, uniqueness
PDF Full Text Request
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