For every number field K, the Riemann hypothesis for ζ_K is equivalent to a specific o(q^{3/4-ε}) error term in the convergence of the discrete measures m_q to the measure κ/ζ_K(2) q dq.
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Discrete Measures and the Extended Riemann Hypothesis
For every number field K, the Riemann hypothesis for ζ_K is equivalent to a specific o(q^{3/4-ε}) error term in the convergence of the discrete measures m_q to the measure κ/ζ_K(2) q dq.