2018/12/11 by Balazard, Michel
#11M26 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1812.04309
In this mainly expository article, we revisit some formal aspects of Báez-Duarte's criterion for the Riemann hypothesis. In particular, starting from Weingartner's formulation of the criterion, we define an arithmetical function ν, which is equal to the Möbius function if, and only if the Riemann hypothesis is true. We record the basic properties of the Dirichlet series of ν, and state a few questions. KEYWORDS: Riemann hypothesis, arithmetical functions, Dirichlet series, Hilbert space