A Hardy space analysis of the Riemann hypothesis

Abstract

The goal of this project is to study the Riemann Hypothesis (RH) using tools from the theory of the Hardy-Hilbert space of holomorphic functions on the unit disk with square summable power series representations. In particular a Hardy space reformulation of the Riemann hypothesis as a completeness problem is taken as the starting point and then tools from operator theory and sub Hardy-Hilbert spaces like the local Dirichlet spaces and Debranges-Rovnyak spaces are utilized to explore Riemann hypothesis realted findings.