Some \(q\)-shift difference results on Hayman conjecture and uniqueness theorems. (English) Zbl 1494.30067
Summary: In this paper, we investigate the value distributions of linear \(q\)-difference polynomials \(f^n(z)+\sum^l_{j=1}a_j(z)f(q_jz+c_j)\) and \(f^n(z)\sum^l_{j=1}a_j(z)f(q_jz+c_j)\) when \(f\) is a transcendental meromorphic function of zero order. The uniqueness theorems of \(q\)-difference polynomials were also considered.
MSC:
| 30D35 | Value distribution of meromorphic functions of one complex variable, Nevanlinna theory |
| 39A10 | Additive difference equations |
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