Andrei Seymour-Howell

Numerical computations of the Riemann zeta function

The Riemann Hypothesis is one of the most famous open problems in mathematics, asserting that the non-trivial zeros of the Riemann zeta function all lie on the line 1/2 + it. Whilst no proof has yet to be found 🙁 , it has been numerically verified for the first 10^13 zeros, with some extra zeros even being computed around the t=10^34 area! Surprisingly, however, all computations have relied on the same method for verification developed by Alan Turing in the 1950's when electronic computations were just getting started. In this talk, I will describe the basic ideas of how to compute the Riemann zeta function and how one goes about numerically verifying the Riemann Hypothesis up to some height.