关于微分-差分多项式的零点和唯一性

doi:10.6040/j.issn.1671-9352.0.2020.559

摘要/Abstract

摘要： 利用Nevanlinna值分布理论,研究零级超越整函数的微分-差分多项式［f(qz+c)ⁿ∏^m_j=1 f ^(j)(z)］^(k)关于小函数α(z)的零点分布,其中n、 j、m、k都是正整数且n≥(m(m+5))/2+k+2;此外,得到了2个零级超越整函数的微分-差分多项式［f(qz+c)ⁿ∏^m_j=1 f ^(j)(z)］^(k)与［g(qz+c)ⁿ∏^m_j=1g^(j)(z)］^(k)CM分担一个值的唯一性结果,其中n、j、m、k都是正整数且n≥(m(m+7))/2+2k+5。

关键词: 零点, 唯一性, q-位移, 微分-差分多项式

Abstract: By Nevanlinna value distribution theory, this paper investigates the zeros distribution of a differential-difference polynomial of a transcendental entire function with zero order ［f(qz+c)ⁿ∏^m_j=1f ^(j)(z)］^(k) concerning a small function α(z), where n,j,m,k are positive integers and n≥(m(m+5))/2+k+2. Furthermore, the uniqueness result of a differential-difference polynomial ［f(qz+c)ⁿ∏^m_j=1f ^(j)(z)］^(k) sharing one value with the other differential-difference polynomial ［g(qz+c)ⁿ∏^m_j=1g^(j)(z)］^(k) is obtained, where n,j,m,k are positive integers and n≥(m(m+7))/2+2k+5.

Key words: zeros, uniqueness, q-shift, differential-difference polynomial

中图分类号:

O174.5

陈文杰,孙桂荣,黄志刚. 关于微分-差分多项式的零点和唯一性[J]. 《山东大学学报(理学版)》, 2021, 56(4): 57-65.

CHEN Wen-jie, SUN Gui-rong, HUANG Zhi-gang. On zeros and uniqueness of differential-difference polynomials[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(4): 57-65.

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