Simultaneous Universality and Simple a-Points of the Riemann Zeta-Function and Its Derivatives

In 1972, Voronin established two theorems concerning a-points of the Riemann zeta-function ζ(s) and its derivatives. Moreover, in 1975, he proved his celebrated universality theorem for ζ(s). In this paper, we discuss a generalization of this universality theorem, and in fact establish a simultaneous universality theorem for ζ(s) and its derivatives. We also investigate the existence and distribution of simple a-points of these functions. In particular, the two theorems of Voronin in 1972, the universality theorem for ζ(s) and some related results are connected and improved.