Simultaneous joint universality of Dirichlet L-functions and their derivatives, with applications

Abstract

We establish a simultaneous joint universality theorem for Dirichlet L-function and their derivatives. This result unifies and extends the joint universality theorem for Dirichlet L-functions due to Bagchi, Gonek and Voronin, and the simultaneous universality theorem for the Riemann zeta-function and its derivatives recently obtained by the author. As an application of this generalized universality, we investigate the value-distribution of Dirichlet L-function and their derivatives.