### Numerical verification of the Riemann Hypothesis to 3•10^{12}

Heilbronn Number Theory Seminar

3rd June 2020, 4:00 pm – 5:00 pm

Online,

Proving (or disproving) the Riemann Hypothesis still eludes us. What we can do is check all the non-trivial zeros of $\zeta$ below some height $H$ do indeed have real part one half. Riemann checked to about $H=30$ (by hand) and (a century and a half later) the author checked to $H=3\cdot 10^{10}$ (not by hand). Gourdon had earlier reached nearly $H=2.446\cdot 10^{12}$ but his result was never formally published. Feeling sorry for researchers having to chose between a lower published figure and a higher unpublished one, we set about confirming Gourdon's result and going a bit further. This talk will describe how.

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