Arithmetic of Quaternion Groups
| dc.creator | Jahangiri, Majid | |
| dc.date | 2009-02-22 | |
| dc.date | 2009-02-24 | |
| dc.date.accessioned | 2026-07-07T12:45:54Z | |
| dc.date.available | 2026-07-07T12:45:54Z | |
| dc.description | Let $p$ be a prime and $a$ a quadratic non-residue $\bmod p$. Then the set of integral solutions of the diophantine equation $x_0^2 - ax_1^2 -px_2^2 + apx_3^2=1$ form a cocompact discrete subgroup $Γ_{p,a}\subset SL(2,\mathbb{R})$ and is commensurable with the group of units of an order in a quaternion algebra over $\mathbb{Q}$. The problem addressed in this paper is an estimate for the traces of a set of generators for $Γ_{p,a}$. Empirical results summarized in several tables show that the trace has significant and irregular fluctuations which is reminiscent of the behavior of the size of a generator for the solutions of Pell's equation. The geometry and arithmetic of the group of units of an order in a quaternion algebra play a key role in the development of the code for the purpose of this paper. | |
| dc.description | 15 pages; 5 figures | |
| dc.identifier | https://arxiv.org/abs/0902.3794 | |
| dc.identifier | http://arxiv.org/abs/0902.3794 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221201 | |
| dc.subject | Number Theory | |
| dc.subject | 11F06 ; 20H10 | |
| dc.title | Arithmetic of Quaternion Groups | |
| dc.type | text |