Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (2): 717-723.doi: 10.1016/S0252-9602(12)60051-4

• Articles • Previous Articles     Next Articles

RESULTS ON A QUESTION OF ZHANG AND YANG

 LI Sheng, GAO Zong-Sheng   

  1. LMIB &|School of Mathematics and Systems Science, Beihang University, Beijing 100191, China;College of Science, Guangdong Ocean University, Zhanjiang 524088, China LMIB &|School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
  • Received:2010-01-01 Revised:2011-03-03 Online:2012-03-20 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.

Abstract:

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

CLC Number: 

  • 30D35
Trendmd