Robert MacKay

Towards a spectral proof of Riemann’s hypothesis

The talk presents evidence that Riemann’s ξ function evaluated at 2 sqrt{E} might be the characteristic function P(E) for the magnetic Laplacian minus 85/16 on a surface of curvature −1 with magnetic field 9/4, a cusp of width 1, a Dirichlet condition at a point, and some other conditions not yet determined but with respect to which one might hope the operator is Hermitian. It also presents some obstacles, however, to this goal.