Zero-density results: a third-best result towards the Riemann hypothesis

3:00pm, Wednesday, 25-th October

Abstract

Ideally, prove the Riemann hypothesis. But, if this is too hard, then a good second best is: show that no zeroes of the Riemann zeta-function have real parts close to 1. If this is too hard, then a good third best is: show that not too many zeroes of the Riemann zeta-function have real parts close to 1.

I shall give an overview of zero-density estimates, which is the third-best attempt mentioned above. This will include some recent work by colleagues at UNSW Canberra, one excellent idea I had that fails, and another idea for future research.