Abstract
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.
Citation
Laurent Habsieger. "On the Nyman-Beurling criterion for the Riemann hypothesis." Funct. Approx. Comment. Math. 37 (1) 187 - 201, January 2007. https://doi.org/10.7169/facm/1229618750
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