Acta mathematica scientia, Series B >
RESULTS ON A QUESTION OF ZHANG AND YANG
Received date: 2010-01-01
Revised date: 2011-03-03
Online published: 2012-03-20
Supported by
This work is supported by NNSF of China (11171013) and Fundamental Research Funds for the Central Universities NO. 300414. The first author is also supported by the Innovation Foundation of BUAA for Ph.D. Candidates.
For a meromorphic function f, let N(l+1(r, 1/f ) denote the counting function of zeros of f of order l at least. Let f be a nonconstant meromorphic function, such that N(r, f) = S(r, f). Denote F = fn. Suppose that F and F′ share 1 CM. If (1) n ≥ 3, or (2) n = 2 and N(r, 1/
f ) = O(N(3(r, 1/f )), then, F = F′, and f assumes the form
f(z) = ce1/n z,
where c is a nonzero constant. This main result of this article gives a positive answer to a question raised by Zhang and Yang [1] for the meromorphic functions case in some sense. And a relative result is proved.
Key words： Nevanlinna theory; shared value; derivative
LI Sheng , GAO Zong-Sheng . RESULTS ON A QUESTION OF ZHANG AND YANG[J]. Acta mathematica scientia, Series B, 2012 , 32(2) : 717 -723 . DOI: 10.1016/S0252-9602(12)60051-4
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