Characteristic estimation of differential polynomials
Keyword(s):
AbstractIn this paper, we give the characteristic estimation of a meromorphic function f with the differential polynomials $f^{l}(f^{(k)})^{n}$ f l ( f ( k ) ) n and obtain that $$\begin{aligned} T(r,f)\leq M\overline{N} \biggl(r,\frac{1}{f^{l}(f^{(k)})^{n}-a} \biggr)+S(r,f) \end{aligned}$$ T ( r , f ) ≤ M N ‾ ( r , 1 f l ( f ( k ) ) n − a ) + S ( r , f ) holds for $M=\min \{\frac{1}{l-2},6\}$ M = min { 1 l − 2 , 6 } , integers $l(\geq 2)$ l ( ≥ 2 ) , $n(\geq 1)$ n ( ≥ 1 ) , $k(\geq 1)$ k ( ≥ 1 ) , and a non-zero constant a. This quantitative estimate is an interesting and complete extension of earlier results. The value distribution of a differential monomial of meromorphic functions is also investigated.
2005 ◽
Vol 78
(1)
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pp. 17-26
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2016 ◽
Vol 95
(2)
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pp. 238-249
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1995 ◽
Vol 38
(4)
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pp. 490-495
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2013 ◽
Vol 57
(2)
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pp. 493-504
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2011 ◽
Vol 2011
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pp. 1-24