Zeros, poles, and fixed points of meromorphic solutions of difference Painlevé equations (Q1724949)

Summary: In this paper, we mainly study the properties of transcendental meromorphic solutions \(f(z)\) of difference Painlevé equations \(w(z + 1) w(z - 1)(w(z) - 1) = \eta(z) w^2(z) - \lambda(z) w(z)\) and \(w(z + 1) w(z - 1)(w(z) -\)\(1) = \eta(z) w(z)\) and obtain precise estimations of the exponents of convergence of zeros, poles of \(\Delta f(z)\) and \(\Delta f(z) / f(z)\), and of fixed points of \(f(z + c)\) for any \(c \in \mathbb C\).