| The Zeros and Nevanlinna Deficiencies for Some $q$-Shift Difference Differential Polynomials of Meromorphic Functions |
| Received:October 19, 2020 Revised:April 07, 2021 |
| Key Words:
Nevanlinna theory $q$-shift difference differential zero order
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11761035; 12161074), the Natural Science Foundation of Jiangxi Province (Grant No.20181BAB201001) and the Foundation of Education Department of Jiangxi Province (Grant Nos.GJJ190876; GJJ202303; GJJ201813; GJJ191042). |
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| Abstract: |
| The first purpose of this paper is to study the properties on some $q$-shift difference differential polynomials of meromorphic functions, some theorems about the zeros of some $q$-shift difference-differential polynomials with more general forms are obtained. The second purpose of this paper is to investigate the properties on the Nevanlinna deficiencies for $q$-shift difference differential monomials of meromorphic functions, we obtain some relations among $\delta(\infty,f)$, $\delta(\infty,f')$, $\delta(\infty,f(z)^nf(qz+c)^mf'(z))$, $\delta(\infty,f(qz+c)^mf'(z))$ and $\delta(\infty, f(z)^nf(qz+c)^m)$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2022.01.004 |
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