  In this work we show that the Riemann hypothesis for the Dedekind
zeta--function $\zeta_{\mathrm{K}}(s)$ of an algebraic number field
$\mathrm{K}$ is equivalent to a problem of the rate of convergence of certain
discrete measures defined arithmetically on the multiplicative group of
positive real numbers to the measure $\zeta_{\mathrm{K}}(2)^{-1}\kappa q dq $,
where $\kappa$ denotes the residue of $\zeta_{\mathrm{K}}(s)$ at $s=1$ and $dq$
the Lebesgue measure.
