If the Alternative Hypothesis plus the new weak density condition holds, then asymptotically 100% of the non-trivial zeros of the Riemann zeta function are simple and on the critical line.
Brian Conrey
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Pair Correlation Conjecture for the zeros of the Riemann zeta-function II: The Alternative Hypothesis
If the Alternative Hypothesis plus the new weak density condition holds, then asymptotically 100% of the non-trivial zeros of the Riemann zeta function are simple and on the critical line.