Joint weighted universality of the Hurwitz zeta-functions

Joint weighted universality theorems are proved concerning simultaneous approximation of a collection of analytic functions by a collection of shifts of Hurwitz zeta-functions with parameters $\alpha_1,\dots,\alpha_r$. For this, linear independence is required over the field of rational numbers for the set $\{\log(m+\alpha_j)\colon m\in \mathbb{N}_0=\mathbb{N}\cup\{0\}, j=1,\dots,r\}$.