A strengthening of the Nyman-Beurling criterion for the Riemann Hypothesis
| dc.creator | Baez-Duarte, Luis | |
| dc.date | 2002-02-15 | |
| dc.date | 2002-02-18 | |
| dc.date.accessioned | 2026-07-07T04:46:28Z | |
| dc.date.available | 2026-07-07T04:46:28Z | |
| dc.description | Let $ρ(x)=x-[x]$, $χ=χ_{(0,1)}$. In $L_2(0,\infty)$ consider the subspace $\B$ generated by $\{ρ_a | a \geq 1\}$ where $ρ_a(x):=ρ(\frac{1}{ax})$. By the Nyman-Beurling criterion the Riemann hypothesis is equivalent to the statement $χ\in\bar{\B}$. For some time it has been conjectured, and proved in this paper, that the Riemann hypothesis is equivalent to the stronger statement that $χ\in\bar{\Bnat}$ where $\Bnat$ is the much smaller subspace generated by $\{ρ_a | a\in\Nat\}$. | |
| dc.description | 7 pages, 3 typos corrected, one reference added | |
| dc.identifier | https://arxiv.org/abs/math/0202141 | |
| dc.identifier | http://arxiv.org/abs/math/0202141 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63343 | |
| dc.subject | Number Theory | |
| dc.title | A strengthening of the Nyman-Beurling criterion for the Riemann Hypothesis | |
| dc.type | text |