Open Access
January 2007 On the Nyman-Beurling criterion for the Riemann hypothesis
Laurent Habsieger
Funct. Approx. Comment. Math. 37(1): 187-201 (January 2007). DOI: 10.7169/facm/1229618750


The Nyman-Beurling criterion states that the Riemann hypothesis is equivalent to the density in $L^2(0,+\infty;t^{-2} dt)$ of a certain space. We introduce an orthonormal family in $L^2(0,+\infty;t^{-2} dt)$, study the space generated by this family and reformulate the Nyman-Beurling criterion using this orthonormal basis. We then study three approximations that could lead to a proof of this criterion.


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Laurent Habsieger. "On the Nyman-Beurling criterion for the Riemann hypothesis." Funct. Approx. Comment. Math. 37 (1) 187 - 201, January 2007.


Published: January 2007
First available in Project Euclid: 18 December 2008

zbMATH: 1226.11088
MathSciNet: MR2357318
Digital Object Identifier: 10.7169/facm/1229618750

Primary: 11M26
Secondary: ‎46E20‎

Keywords: Nyman-Beurling Criterion , Riemann hypothesis

Rights: Copyright © 2007 Adam Mickiewicz University

Vol.37 • No. 1 • January 2007
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