Uniform Distribution Modulo 1 and the Joint Universality of Dirichlet L -functions

Abstract

In the paper, we prove a joint universality theorem on the approximation of a collection of analytic functions by a collection of shifts of Dirichlet L-functions L(s + iτ, \( \chi \) j ), where \( \tau \) takes values from the set {k α: k = 0, 1, 2, . . . } with 0 < \( \alpha \) < 1. The proof of this theorem uses the theory of uniform distribution modulo 1.