Paired Hayman conjecture and uniqueness of complex delay-differential polynomials. (English) Zbl 1483.30064
Summary: In this paper, the paired Hayman conjecture of different types are considered, namely, the zeros distribution of \(f(z)^nL(g)-a(z)\) and \(g(z)^nL(f)-a(z)\), where \(L(h)\) takes the derivatives \(h^{(k)}(z)\) or the shift \(h(z+c)\) or the difference \(h(z+c)-h(z)\) or the delay-differential \(h^{(k)}(z+c)\), where \(k\) is a positive integer, \(c\) is a non-zero constant and \(a(z)\) is a non-zero small function with respect to \(f(z)\) and \(g(z)\). The related uniqueness problems of complex delay-differential polynomials are also considered.
MSC:
| 30D35 | Value distribution of meromorphic functions of one complex variable, Nevanlinna theory |
| 39A05 | General theory of difference equations |
Keywords:
meromorphic functions; paired Hayman conjecture; delay-differential polynomials; uniquenessReferences:
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