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

Michel Balazard (1)

1 I2M - Institut de Mathématiques de Marseille

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 $\nu$, 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 $\nu$, and state a few questions.

Mots clés: Riemann hypothesis; arithmetical functions; Dirichlet series; Hilbert space

Domaines: Théorie des nombres [math.NT]

Michel Balazard. An arithmetical function related to B\'aez-Duarte’s criterion for the Riemann hypothesis. Michael Th. Rassias. Harmonic Analysis and Applications, 168, Springer, pp.43-58, 2021, Springer Optimization and Its Applications, 978-3-030-61886-5. ⟨hal-01950436⟩