Values of Special Indefinite Quadratic Forms
| dc.creator | Elsner, Guido | |
| dc.date | 2007-03-01 | |
| dc.date.accessioned | 2026-07-07T07:49:35Z | |
| dc.date.available | 2026-07-07T07:49:35Z | |
| dc.description | For special $d$-dimensional hyperbolic shells $E$ with $ d\geq 5$ we show that the number of lattice points in $E$ intersected with a $d$-dimensional cube $C_r$ of edge length $r$, can be approximated by the volume of $E\cap C_r$, as $r$ tends to infinity, up to an error of order ${\mathcal O}(r^{d-2})$. We generalize results and techniques, used by F. Götze (2004), to a large class of {\em indefinite} quadratic forms and we provide explicit bounds for the errors in terms of certain Minkowski minima related to these quadratic forms. Furthermore, we obtain, as in the positive definite case, a result for multivariate diophantine approximation and for the maximal gap between values of such indefinite forms. | |
| dc.description | 39 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0703029 | |
| dc.identifier | http://arxiv.org/abs/math/0703029 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124904 | |
| dc.subject | Number Theory | |
| dc.subject | 11P21 | |
| dc.title | Values of Special Indefinite Quadratic Forms | |
| dc.type | text |