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arXiv · 2004.09765

The Riemann hypothesis is true up to $3\cdot 10^{12}$

Dave Platt·Tim Trudgian
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Abstract

We verify numerically, in a rigorous way using interval arithmetic, that the Riemann hypothesis is true up to height $3\cdot10^{12}$. That is, all zeroes $\beta + i\gamma$ of the Riemann zeta-function with $0<\gamma\leq 3\cdot 10^{12}$ have $\beta = 1/2$.

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Dave Platt, Tim Trudgian. 2020-04-21. The Riemann hypothesis is true up to $3\cdot 10^{12}$. https://doi.org/10.1112/blms.12460

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