The distribution of lattice points in elliptic annuli
| dc.creator | Wigman, Igor | |
| dc.date | 2004-07-04 | |
| dc.date | 2005-08-09 | |
| dc.date.accessioned | 2026-07-07T05:09:56Z | |
| dc.date.available | 2026-07-07T05:09:56Z | |
| dc.description | Let $N(t, ρ)$ be the number of lattice points in a thin elliptical annuli. We assume the aspect ratio $β$ of the ellipse is transcendental and Diophantine in a strong sense (this holds for {\em almost all} aspect ratios). The variance of $N(t, ρ)$ is $t(8πβ\cdot ρ)$. We show that if $ρ$ shrinks slowly to zero then the distribution of the normalized counting function $\frac{N(t, ρ) - A(2tρ+ρ^2)}{\sqrt{8 πβ\cdot t ρ}}$ is Gaussian, where A is the area of the ellipse. The case of \underline{circular} annuli is due to Hughes and Rudnick. | |
| dc.identifier | https://arxiv.org/abs/math/0407049 | |
| dc.identifier | http://arxiv.org/abs/math/0407049 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71770 | |
| dc.subject | Number Theory | |
| dc.title | The distribution of lattice points in elliptic annuli | |
| dc.type | text |