An arithmetical function related to B\'aez-Duarte's criterion for the Riemann hypothesis
Number Theory
2018-12-12 v1
Abstract
In this mainly expository article, we revisit some formal aspects of B{\'a}ez-Duarte's criterion for the Riemann hypothesis. In particular, starting from Weingartner's formulation of the criterion, we define an arithmetical function , which is equal to the M{\"o}bius function if, and only if the Riemann hypothesis is true. We record the basic properties of the Dirichlet series of , and state a few questions. KEYWORDS: Riemann hypothesis, arithmetical functions, Dirichlet series, Hilbert space
Keywords
Cite
@article{arxiv.1812.04309,
title = {An arithmetical function related to B\'aez-Duarte's criterion for the Riemann hypothesis},
author = {Michel Balazard},
journal= {arXiv preprint arXiv:1812.04309},
year = {2018}
}
Comments
Harmonic Analysis and Applications (Michael Th. Rassias, ed.), In press