JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (4): 57-65.doi: 10.6040/j.issn.1671-9352.0.2020.559

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On zeros and uniqueness of differential-difference polynomials

CHEN Wen-jie, SUN Gui-rong, HUANG Zhi-gang*   

  1. School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China
  • Published:2021-04-13

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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∏mj=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∏mj=1f (j)(z)］(k) sharing one value with the other differential-difference polynomial ［g(qz+c)n∏mj=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

CLC Number: 

  • O174.5
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