A general strong Nyman-Beurling Criterion for the Riemann Hypothesis
| dc.creator | Baez-Duarte, Luis | |
| dc.date | 2005-05-22 | |
| dc.date.accessioned | 2026-07-07T05:20:08Z | |
| dc.date.available | 2026-07-07T05:20:08Z | |
| dc.description | For each $f:[0,\infty)\to\Com$ formally consider its co-Poisson or Müntz transform $g(x)=\sum_{n\geq 1}f(nx)-\frac{1}{x}\int_0^\infty f(t)dt$. For certain $f$'s with both $f, g \in L_2(0,\infty)$ it is true that the Riemann hypothesis holds if and only if $f$ is in the $L_2$ closure of the vector space generated by the dilations $g(kx)$, $k\in\Nat$. Such is the case for example when $f=χ_{(0,1]}$ where the above statement reduces to the strong Nyman criterion already established by the author. In this note we show that the necessity implication holds for any continuously differentiable function $f$ vanishing at infinity and satisfying $\int_0^\infty t|f'(t)|dt<\infty$. If in addition $f$ is of compact support then the sufficiency implication also holds true. It would be convenient to remove this compactness condition. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0505453 | |
| dc.identifier | http://arxiv.org/abs/math/0505453 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75268 | |
| dc.subject | Number Theory | |
| dc.title | A general strong Nyman-Beurling Criterion for the Riemann Hypothesis | |
| dc.type | text |