一类微分多项式的零点分布的研究
The Zeros of Some Differential Polynomials

作者: 杨 静 * , 王文博 :中国石油大学(华东)理学院,山东 青岛;

关键词: 整函数微分多项式零点值分布Entire Function Differential Polynomial Zero Value Distribution

摘要:
本文采用亚纯函数值分布理论作为工具,讨论了微分多项式ff''+a(f')2+b的零点分布情况,该结论推广了Hayman,Mues和Tohge等人的相关结果。

Abstract: In this paper, we use the Nevanlinna theory and discuss the zeros of ff''+a(f')2+b. This result generalizes the related results of Hayman, Mues and Tohge et al.

文章引用: 杨 静 , 王文博 (2016) 一类微分多项式的零点分布的研究。 理论数学, 6, 223-226. doi: 10.12677/PM.2016.63035

参考文献

[1] Hayman, W.K. (1964) Meromorphic Functions. Clarendon Press, Oxford.

[2] Yang, L. (1993) Value Distribution Theory. Springer, Berlin.

[3] Yang, C.C. and Yi, H.X. (2003) Uniqueness Theory Meromorphic Functions. Kluwer Academic Publishers, Dordrecht.
http://dx.doi.org/10.1007/978-94-017-3626-8

[4] Hayman, W.K. (1959) Picard Values of Meromorphic Functions and Their Derivatives. Annals of Mathematics, 70, 9-42.
http://dx.doi.org/10.2307/1969890

[5] Hayman, W.K. (1967) Research Problems in Function Yheory. The Athlone Press University of London, London.

[6] Mues, E. (1979) Über ein Problem von Hayman. Mathematische Zeitschrift, 164, 239-259.
http://dx.doi.org/10.1007/BF01182271

[7] Ozawa, M. (1989) Zeros of Certain Differential Polynomials. Analytic Function Theory of One Complex Variable. Pitman Research Notes in Mathematics Series, 212, 199-225.

[8] Lehners, G. (1984) Ube Nullstellenfreie Homogene Differentialpolynome. Dissertaion, Fath-Bereich Mathematik der Universitat Hannover.

[9] Tohge, K. (1993) On the Zeros of a Homogeneous Differential Polynomial. Kodai Mathematical Journal, 16, 398-415.
http://dx.doi.org/10.2996/kmj/1138039848

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