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Answer by user111966 for What are the implications of a zero of zeta off the...

Perhaps this is a duplicate of this question If the Riemann Hypothesis fails, must it fail infinitely often?.The discussion continues here The Hardy Z-function and failure of the Riemann hypothesis,...

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Answer by GH from MO for What are the implications of a zero of zeta off the...

1. First, let us get history right: Hardy (1914) proved there are infinitely many zeros on the critical line, Hardy-Littlewood (1921) proved there are $\gg T$ zeros on the critical line up to height...

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What are the implications of a zero of zeta off the critical line

So what happens if there is a non-trivial zero of the Riemann zeta function off the critical line? Has there been any work in the following direction: We know from Landaus theorem that there is a...

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