An Arithmetical Function Related to Báez-Duarte’s Criterion for the Riemann Hypothesis

Michel Balazard ()
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Michel Balazard: Aix-Marseille University, CNRS, Centrale Marseille

A chapter in Harmonic Analysis and Applications, 2021, pp 43-58 from Springer

Abstract: Abstract 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-61887-2_3

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DOI: 10.1007/978-3-030-61887-2_3

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