On Good Universality and the Riemann Hypothesis

We use subsequence ergodic theorems applied to Boole's transformation and its variants and their invariant measures on the real line to give new characterisations of the Lindelhof Hypothesis and the Riemann hypothesis. This builds on earlier work of R. L. Adler and B. Weiss, M. Lifshits and M. Weber, J. Steuding, J. Lee and A. I. Surijaya using Birkhoff's ergodic theorem and probability theory. The talk is on work with Jean-Louis Verger-Gaugry and Michel Weber.