Discrete Measures and the Extended Riemann Hypothesis
In this work we show that the Riemann hypothesis for the Dedekind zeta--function $ζ_{\mathrm{K}}(s)$ 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 $ζ_{\mathrm{K}}(2)^{-1}κq dq $, where $κ$ denotes the residue of $ζ_{\mathrm{K}}(s)$ at $s=1$ and $dq$ the Lebesgue measure.
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