Two generalizations of Liouville λ function

Abstract

We study the properties of two classes of functions $\lambda_k$ and $\tilde{\lambda}_k$ that generalize the Liouville $\lambda$ function, including some equivalencies between the Riemann hypothesis and some assertions about the asymptotic behavior of the summatory functions of $\lambda_k$ and $\tilde{\lambda}_k.$ Similar results are obtained for the generalization of the Möbius function considered by Tanaka.