中国综合性科技类核心期刊(北大核心)

中国科学引文数据库来源期刊(CSCD)

美国《化学文摘》(CA)收录

美国《数学评论》(MR)收录

俄罗斯《文摘杂志》收录

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一类差分多项式的零点和唯一性

王乙萍 黄志刚

王乙萍, 黄志刚. 一类差分多项式的零点和唯一性[J]. 华东师范大学学报(自然科学版), 2021, (1): 28-35. doi: 10.3969/j.issn.1000-5641.201911044
引用本文: 王乙萍, 黄志刚. 一类差分多项式的零点和唯一性[J]. 华东师范大学学报(自然科学版), 2021, (1): 28-35. doi: 10.3969/j.issn.1000-5641.201911044
WANG Yiping, HUANG Zhigang. Zeros and uniqueness of a class of difference polynomials[J]. Journal of East China Normal University (Natural Sciences), 2021, (1): 28-35. doi: 10.3969/j.issn.1000-5641.201911044
Citation: WANG Yiping, HUANG Zhigang. Zeros and uniqueness of a class of difference polynomials[J]. Journal of East China Normal University (Natural Sciences), 2021, (1): 28-35. doi: 10.3969/j.issn.1000-5641.201911044

一类差分多项式的零点和唯一性

doi: 10.3969/j.issn.1000-5641.201911044
基金项目: 国家自然科学基金(11971344); 苏州科技大学研究生科研创新计划(SKCX18-Y03)
详细信息
    通讯作者:

    黄志刚, 男, 教授, 研究方向为复分析. E-mail: hzg@mail.usts.edu.cn

  • 中图分类号: O174.52

Zeros and uniqueness of a class of difference polynomials

  • 摘要: 主要运用Nevanlinna值分布理论研究了差分多项式的唯一性和零点分布, 得到了关于差分多项式$P(f)\sum_{i=1}^{k}t_{i}f(z+c_{i})$的唯一性结果和关于差分多项式$P(f)\big(\sum_{i=1}^{k}b_{i}(z)f(z+c_{i})\big)^s-b_0(z)$的零点分布结果, 其中$f(z)$是有限级超越整函数, $c_{i}, t_{i}\;(i=1,2, \cdots, k)$是非零复常数, $b_{i}(z)\;(i=0, 1, \cdots, k)$是关于$f(z)$的小函数.
  • [1] HAYMAN W K. Meromorphic Functions [M]. Oxford: Clarendon Press, 1964.
    [2] LAINE I. Nevanlinna Theory and Complex Differential Equations [M]. Berlin: Walter de Gruyter, 1993.
    [3] YANG L. Value Distribution Theory [M]. Berlin: Springer-Verlag, Science Press, 1993.
    [4] YANG C C, YI H X. Uniqueness Theory of Meromorphic Functions [M]. Beijing: Science Press, 2003.
    [5] LUO X D, LIN W C. Value sharing results for shifts of meromorphic functions [J]. Journal of Mathematical Analysis and Applications, 2011, 377(2): 441-449.
    [6] HAYMAN W K. Picard values of meromorphic functions and their derivatives [J]. Annals of Mathematics, 1959, 70(1): 9-42. DOI:  10.2307/1969890.
    [7] HALBURD R, KORHONEN R, TOHGE K. Holomorphic curves with shift-invariant hyperptane preimages [J]. Transactions of the American Mathematical Society, 2009, 366(8): 4267-4298.
    [8] CHIANG Y M, FENG S J. On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane [J]. Ramanujan Journal, 2006, 16(1): 105-129.
    [9] LAINE I, YANG C C. Clunie theorems for difference and q-difference polynomials [J]. Journal of the London Mathematical Society, 2007, 76(3): 556-566. DOI:  10.1112/jlms/jdm073.
    [10] LAINE I, YANG C C. Value distribution of difference polynomials [J]. Proc Japan Acad (A), 2007, 83: 148-151.
    [11] QI X G, YANG L Z, LIU K. Uniqueness and periodicity of meromorphic functions concerning the difference operator [J]. Computers and Mathematics with Applications, 2010, 60(6): 1739-1746. DOI:  10.1016/j.camwa.2010.07.004.
    [12] LIU Y, QI X G, YI H X. Value distribution of difference polynomials of meromorphic functions [J]. Electronic Journal of Differential Equations, 2013, 269: 1-9.
    [13] QI X G, LIU K. Uniqueness and value distribution of differences of entire functions [J]. Journal of Mathematical Analysis and Applications, 2011, 379(1): 180-187. DOI:  10.1016/j.jmaa.2010.12.031.
    [14] KORHONEN R. A new Clunie type theorem for difference polynomials [J]. Journal of Difference Equations and Applications, 2011, 17(3): 387-400.
    [15] 刘礼培. 亚纯函数分担多项式的唯一性 [J]. 江西师范大学学报(自然科学版), 2010, 34(3): 262-266.
    [16] 周利利, 黄志刚, 孙桂荣. 关于复域差分的值分布 [J]. 华东师范大学学报(自然科学版), 2015(3): 1-8.
    [17] QI X G, DOU J, YANG L Z. The properties of solutions of certain type of difference equations [J]. Advances in Difference Equations, 2014, 2014: 256.
    [18] LAINE I. Zero distribution of some shift polynomials [J]. Journal of Mathematical Analysis and Applications, 2019, 469(2): 808-826.
    [19] YANG L Z, ZHANG J L. Non-existence of meromorphic solutions of a Fermat type functional equation [J]. Aequationes Mathematicae, 2008, 76(1): 140-150.
  • 加载中
计量
  • 文章访问数:  114
  • HTML全文浏览量:  63
  • PDF下载量:  11
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-11-07
  • 刊出日期:  2021-01-27

目录

    /

    返回文章
    返回