Fourier interpolation from zeros of the Riemann zeta function

Abstract: I will talk about a recent result that any sufficiently nice even analytic function can be recovered from its values at the nontrivial zeros of zeta(1/2+is) and the values of its Fourier transform at logarithms of positive integers. The proof is based on an explicit interpolation formula, whose construction relies on a strengthening of Knopp's abundance principle for Dirichlet series with functional equations. The talk is based on a joint work with Andriy Bondarenko and Kristian Seip.