A Hardy space analysis of the B\'aez-Duarte criterion for the RH

TL;DR

This paper employs advanced functional analysis techniques from sub-Hardy Hilbert spaces to explore Bez-Duarte's reformulation of the Riemann hypothesis, aiming to shed light on this longstanding mathematical conjecture.

Contribution

It introduces a novel approach using Hardy space analysis to study the Bez-Duarte criterion for the Riemann hypothesis, connecting complex analysis with number theory.

Findings

New insights into the Bez-Duarte criterion via Hardy space methods

Potential implications for the Riemann hypothesis

Extension of sub-Hardy space techniques to number theory

Abstract

In this article, methods from sub-Hardy Hilbert spaces such as the de Branges-Rovnyak spaces and local Dirichlet spaces are used to investigate B\'aez-Duarte's Hilbert space reformulation of the Riemann hypothesis (RH).