Associating curves of low genus to infinite nilpotent groups via the zeta function
| dc.creator | Griffin, Cornelius | |
| dc.date | 2002-09-20 | |
| dc.date.accessioned | 2026-07-07T04:51:04Z | |
| dc.date.available | 2026-07-07T04:51:04Z | |
| dc.description | It is known from work of du Sautoy and Grunewald in \cite{duSG1} that the zeta functions counting subgroups of finite index in infinite nilpotent groups depend upon the behaviour of some associated system of algebraic varieties on reduction $\modp.$ Further to this, in \cite{duS3, duS4} du Sautoy constructed a group whose local zeta function was determined by the number of points on the elliptic curve $E:Y^2=X^3-X.$ In this work we generalise du Sautoy\rq s construction to define a class of groups whose local zeta functions are dependent upon the number of points on the reduction of a given elliptic curve with a rational point. We also construct a class of groups that behave the same way in relation to any curve of genus 2 with a rational point. We end with a discussion of problems arising from this work. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/math/0209271 | |
| dc.identifier | http://arxiv.org/abs/math/0209271 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65018 | |
| dc.subject | Number Theory | |
| dc.subject | 11M41 | |
| dc.title | Associating curves of low genus to infinite nilpotent groups via the zeta function | |
| dc.type | text |