Dave Platt

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

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 Feeling sorry for researchers having to chose between a lower published figure and a higher unpublished one, we set about confirming Gourdon's result and going a bit further.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.