| 郑秀敏,吴顺周.有限级超越整函数的差分多项式的值分布[J].数学年刊A辑,2016,37(2):115~126 |
| 有限级超越整函数的差分多项式的值分布 |
| Value Distribution of Difference Polynomials of Transcendental Entire Functions of Finite Order |
| Received:May 30, 2015 Revised:September 06, 2015 |
| DOI： |
| 中文关键词: 差分多项式, 整函数, 值分布 |
| 英文关键词:Difference polynomial, Entire function, Value
distribution |
| 基金项目:本文受到国家自然科学基金(No.11301233, No.11171119), 江西省自然科学基金(No.20151BAB201004)
和江西省教育厅青年科学基金(No.GJJ14271)的资助 |
|
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| 中文摘要: |
| 研究了差分多项式$$H(z) = P(f)\sum\limits_{i=1}^ka_if(z+c_i) $$
的值分布, 其中$f$是有限级超越整函数, $P(f)$是$f$的多项式, $k\geq2$,\ \ $c_i\ (i=1,\cdots,k)$是互不相同的常数, $a_i\ (i=1,\cdots, k)$是非零常数. 得到了
$H(z)-a$和$H(z)-\alpha(z)$的零点的个数的估计, 其中$a\in\mathbb{C}$且$\alpha(z)\ (\not\equiv0)$为小函数.
讨论了$H(z)$的非零有限Borel例外值的不存在性. |
| 英文摘要: |
| This paper deals with the value distribution
of the difference polynomial
$$
H(z) = P(f)\sum\limits_{i=1}^ka_if(z+c_i),
$$
where $f$ is a transcendental entire function of finite order, $P(f)$ is a polynomial of $f$,
$k\geq2,\ c_i\ (i=1,\cdots,k)$ are distinct constants, and $a_i\ (i=1,\cdots,k)$
are non-zero constants. The authors estimate the number of the zeros
of $H(z)-a$ and $H(z)-\alpha(z)$, where $a\in\mathbb{C}$ and
$\alpha(z)\ (\not\equiv0)$ is a small function, and discuss the
non-existence of the non-zero finite Borel exceptional value of
$H(z)$. |
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