The Riemann hypothesis is true up to 3•1012

We verify numerically, in a rigorous way using interval arithmetic, that the Riemann hypothesis is true up to height 3 center dot 1012. That is, all zeroes beta+i gamma of the Riemann zeta-function with 0<= 3 center dot 1012 have beta=1/2. Moreover, all of these zeroes are simple.

Automated summary

The researchers rigorously verified the Riemann hypothesis up to height 3·1012 using interval arithmetic, showing that all the zeros of the Riemann zeta-function at this height have a specific property and are simple.