Arithmetic partial differential equations
| dc.creator | Buium, Alexandru | |
| dc.creator | Simanca, Santiago R. | |
| dc.date | 2006-05-03 | |
| dc.date | 2006-05-10 | |
| dc.date.accessioned | 2026-07-07T07:13:54Z | |
| dc.date.available | 2026-07-07T07:13:54Z | |
| dc.description | We develop an arithmetic analogue of linear partial differential equations in two independent ``space-time'' variables. The spatial derivative is a Fermat quotient operator, while the time derivative is the usual derivation. This allows us to ``flow'' integers or, more generally, points on algebraic groups with coordinates in rings with arithmetic flavor. In particular, we show that elliptic curves have certain canonical ``flows'' on them that are the arithmetic analogues of the heat and wave equations. The same is true for the additive and the multiplicative group. | |
| dc.description | Updated version of paper includes new results on transcendence | |
| dc.identifier | https://arxiv.org/abs/math/0605107 | |
| dc.identifier | http://arxiv.org/abs/math/0605107 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112651 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Rings and Algebras | |
| dc.subject | 11E95, 11G07 | |
| dc.title | Arithmetic partial differential equations | |
| dc.type | text |