ON GOOD UNIVERSALITY AND THE RIEMANN HYPOTHESIS
Résumé
We use subsequence and moving average ergodic theorems applied to Boole's transformation and its variants and their invariant measures on the real line to give new characterisations of the Lindelhöf Hypothesis and the Riemann hypothesis. These ideas are then used to study the value distribution of Dirichlet L series, and the zeta functions of Dedekind, Hurwitz and Riemann and their derivatives. This builds on earlier work of R. L. Adler and B. Weiss, M. Lifshits and M. Weber, J. Steuding, J. Lee and A. I. Suriajaya using Birkhoff's ergodic theorem and probability theory.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)