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http://dx.doi.org/10.4134/BKMS.b210170

PAIRED HAYMAN CONJECTURE AND UNIQUENESS OF COMPLEX DELAY-DIFFERENTIAL POLYNOMIALS  

Gao, Yingchun (Department of Mathematics Nanchang University)
Liu, Kai (Department of Mathematics Nanchang University)
Publication Information
Bulletin of the Korean Mathematical Society / v.59, no.1, 2022 , pp. 155-166 More about this Journal
Abstract
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 nonzero small function with respect to f(z) and g(z). The related uniqueness problems of complex delay-differential polynomials are also considered.
Keywords
Paired Hayman conjecture; uniqueness; meromorphic functions; Delay-differential polynomials;
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