PAIRED HAYMAN CONJECTURE AND UNIQUENESS OF COMPLEX DELAY-DIFFERENTIAL POLYNOMIALS

In this paper, the paired Hayman conjecture of different types are considered, namely, the zeros distribution of f(z)(n) L(g) - a(z) and g(z)(n) L(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.