An arithmetical function related to B\'aez-Duarte's criterion for the Riemann hypothesis

Abstract

In this mainly expository article, we revisit some formal aspects of B{\'a}ez-Duarte's criterion for the Riemann hypothesis. In particular, starting from Weingartner's formulation of the criterion, we define an arithmetical function $\nu$, which is equal to the M{\"o}bius function if, and only if the Riemann hypothesis is true. We record the basic properties of the Dirichlet series of $\nu$, and state a few questions. KEYWORDS: Riemann hypothesis, arithmetical functions, Dirichlet series, Hilbert space