| 陈美茹,陈宗煊.有穷级整函数的差分多项式的性质[J].数学年刊A辑,2012,33(3):359~374 |
| 有穷级整函数的差分多项式的性质 |
| Properties of Difference Polynomials of Entire Functions with Finite Order |
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| DOI： |
| 中文关键词: 整函数 差分多项式 有穷级 唯一性 |
| 英文关键词:Entire function, Difference polynomial, Finite order, Uniqueness |
| 基金项目:国家自然科学基金 |
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| 中文摘要: |
| 考虑了差分多项式f(z)n(f(z)m-1)dΠj=1f(z+cj)vj-α(z)的零点问题,其中f(z)是有穷级的超越整函数.cj(cj≠0,j=1,…,d)是互相判别的常数,n,m,d,vj(j=1,…,d)∈N+,α(z)是f(z)的小函数.还讨论了差分多项式的唯一性问题. |
| 英文摘要: |
| The authors consider the zeros of difference polynomial
$$
f(z)^{n}(f(z)^{m}-1)\prod\limits_{j=1}^{d}f(z+c_{j})^{ c_{j} \nu_{j}}-\alpha(z),
$$
where $f(z)$ is a transcendental entire function with finite order, $c_{j}\ (c_{j} \neq 0,\ j=1,\cdots, d)
$ are distinct constants, $n, m, d,\nu_{j}\ (j=1,\cdots, d)\in\mathbb{N_{+}}$, $\alpha(z)$ is a small function with respect to $f(z)$.
The uniqueness problem on difference polynomials is also discussed. |
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