  We study the value-distribution of the Hurwitz zeta-function with algebraic
irrational parameter $\zeta(s;\alpha)=\sum_{n\geq_0}(n+\alpha)^{-s}$. In
particular, we prove effective denseness results of the Hurwitz zeta-function
and its derivatives in suitable strips containing the right boundary of the
critical strip $1+i\mathbb{R}$. This may be considered as a first "weak"
manifestation of universality for those zeta-functions.
