Functiones et Approximatio Commentarii Mathematici

On the Nyman-Beurling criterion for the Riemann hypothesis

Laurent Habsieger

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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.

Article information

Funct. Approx. Comment. Math., Volume 37, Number 1 (2007), 187-201.

First available in Project Euclid: 18 December 2008

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Zentralblatt MATH identifier

Primary: 11M26: Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
Secondary: 46E20: Hilbert spaces of continuous, differentiable or analytic functions

Riemann hypothesis Nyman-Beurling criterion


Habsieger, Laurent. On the Nyman-Beurling criterion for the Riemann hypothesis. Funct. Approx. Comment. Math. 37 (2007), no. 1, 187--201. doi:10.7169/facm/1229618750.

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