On the Nyman-Beurling criterion for the Riemann hypothesis
Habsieger, Laurent
Funct. Approx. Comment. Math., Tome 37 (2007) no. 1, p. 187-201 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2007-01-15
Classification:  Riemann hypothesis,  Nyman-Beurling criterion,  11M26,  46E20 
@article{1229618750,
     author = {Habsieger, Laurent},
     title = {On the Nyman-Beurling criterion for the Riemann hypothesis},
     journal = {Funct. Approx. Comment. Math.},
     volume = {37},
     number = {1},
     year = {2007},
     pages = { 187-201},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1229618750}
}

Habsieger, Laurent. On the Nyman-Beurling criterion for the Riemann hypothesis. Funct. Approx. Comment. Math., Tome 37 (2007) no. 1, pp.  187-201. http://gdmltest.u-ga.fr/item/1229618750/