Pair correlation densities of inhomogeneous quadratic forms II
| dc.creator | Marklof, Jens | |
| dc.date | 2002-10-14 | |
| dc.date.accessioned | 2026-07-07T04:51:54Z | |
| dc.date.available | 2026-07-07T04:51:54Z | |
| dc.description | Denote by $\| \cdot \|$ the euclidean norm in $\RR^k$. We prove that the local pair correlation density of the sequence $\| \vecm -\vecalf \|^k$, $\vecm\in\ZZ^k$, is that of a Poisson process, under diophantine conditions on the fixed vector $\vecalf\in\RR^k$: in dimension two, vectors $\vecalf$ of any diophantine type are admissible; in higher dimensions ($k>2$), Poisson statistics are only observed for diophantine vectors of type $κ<(k-1)/(k-2)$. Our findings support a conjecture of Berry and Tabor on the Poisson nature of spectral correlations in quantized integrable systems. | |
| dc.identifier | https://arxiv.org/abs/math/0210198 | |
| dc.identifier | http://arxiv.org/abs/math/0210198 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65277 | |
| dc.subject | Number Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Dynamical Systems | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Pair correlation densities of inhomogeneous quadratic forms II | |
| dc.type | text |