一类缓慢增长的亚纯函数微分多项式的例外集

Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (4): 728-734.

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The Exceptional Set for the Differential Polynomials of a Class of Slowly Growing Meromorghic Function

TAN Wei-Ping, ZHAN Xiao-Ping

Department of Mathematics, Hunan First Normal University, Changsha |410205

Received:2012-01-09 Revised:2013-04-12 Online:2013-08-25 Published:2013-08-25
Supported by:
湖南省教育厅科研基金(09C228)资助

Abstract

Abstract:

The value distribution of differential polynomials f ^kQ[f] in meromorphic function f(z) was studied from a viewpoint of exceptional set. We prove the following result. Suppose that f is a transcendental meromorphic function such that δ(∞, f)≥1-α>0. Then if T(r, f)=O((log r)²), f ^kQ[f] asumes any non-zero finite complex number infinitely often outside the union of the discs, where k>1+α(1+Γ_Q)/1-α.

Key words: Entire function, Meromorphic function, Exceptional set, Differential polynomial, ε set

CLC Number:

30M

TAN Wei-Ping, ZHAN Xiao-Ping. The Exceptional Set for the Differential Polynomials of a Class of Slowly Growing Meromorghic Function[J].Acta mathematica scientia,Series A, 2013, 33(4): 728-734.

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The Exceptional Set for the Differential Polynomials of a Class of Slowly Growing Meromorghic Function

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