Two generalizations of Liouville λ function

André Pierro de Camargo
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 1, Pages 30–39
DOI: 10.7546/nntdm.2023.29.1.30-39
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Authors and affiliations

André Pierro de Camargo
Federal University of the ABC region, Brazil


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.


  • Liouville function
  • Möbius function
  • Prime Number Theorem
  • Riemann Hypothesis

2020 Mathematics Subject Classification

  • 11N56
  • 11N99


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Manuscript history

  • Received: 6 September 2022
  • Revised: 15 December 2022
  • Accepted: 10 February 2023
  • Online First: 13 February 2023

Copyright information

Ⓒ 2023 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Camargo, A. P. (2023). Two generalizations of Liouville λ function. Notes on Number Theory and Discrete Mathematics, 29(1), 30-39, DOI: 10.7546/nntdm.2023.29.1.30-39.

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