An asymptotic formula for representations of integers by indefinite hermitian forms
We fix a maximal order O in F = R, C or H, and an F-hermitian form Q of signature (n, 1) with coefficients in O. Let k ∈ N. By applying a lattice point theorem on an n-dimensional F-hyperbolic space, we give an asymptotic formula with an error term, as t → +∞, for the number Nt;(Q,-k) of integral so...
| Autor: | |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/39855 |
| Acceso en línea: | http://hdl.handle.net/11336/39855 |
| Access Level: | acceso abierto |
| Palabra clave: | Hyperbolic Lattice Point Theorem Representation by Hermitian Forms https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | We fix a maximal order O in F = R, C or H, and an F-hermitian form Q of signature (n, 1) with coefficients in O. Let k ∈ N. By applying a lattice point theorem on an n-dimensional F-hyperbolic space, we give an asymptotic formula with an error term, as t → +∞, for the number Nt;(Q,-k) of integral solutions x ∈ On+1 of the equation Q[x] = -k satisfying |xn+1| ≤ t. |
|---|