有理型函数の微分多項式の値分布について

概要

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In the value distribution theory of meromorphic functions, the relative growth of a given function and its derivative playsa very important role. Since R. Nevanlinna proved the importance of the logarithmic derivative f'/f of a meromorphicfunction f in his theory of value distribution in 1925, a number of interesting results of the relative growth of meromorphic functions and their derivatives have been found out. Furthermore, many mathematicians have recently investigated the value distribution of the differential `polynomials' with respect to meromorphic functions. In 1973, Gopalakrishna andBhoosnurmath gave some estimations of the relative growth of meromorphic functions and their homogeneous differentialpolynomials. However their results have an unnecessary condition; the `homogeneousness' of the polynomials. In this paper we consider all differential polynomials of transcendental meromorphic functions on the complex plane, and we give some ( upper and lower ) estimations of comparative growth of the characteristic functions of meromorphic functions and theirdifferential polynomials. Our results extend the result of Gopalakrishna and Bhoosnurmath.
東京都立産業技術高等専門学校の論文