A lower bound for the height of a rational function at $S$-unit points
| dc.creator | Corvaja, Pietro | |
| dc.creator | Zannier, Umberto | |
| dc.date | 2003-11-04 | |
| dc.date | 2004-04-22 | |
| dc.date.accessioned | 2026-07-07T05:02:27Z | |
| dc.date.available | 2026-07-07T05:02:27Z | |
| dc.description | Let $Γ$ be a finitely generated subgroup of the multiplicative group $\G_m^2(\bar{Q})$. Let $p(X,Y),q(X,Y)\in\bat{Q}$ be two coprime polynomials not both vanishing at $(0,0)$; let $ε>0$. We prove that, for all $(u,v)\inΓ$ outside a proper Zariski closed subset of $G_m^2$, the height of $p(u,v)/q(u,v)$ verifies $h(p(u,v)/q(u,v))>h(1:p(u,v):q(u,v))-ε\max(h(uu),h(v))$. As a consequence, we deduce upper bounds for (a generalized notion of) the g.c.d. of $u-1,v-1$ for $u,v$ running over $Γ$. | |
| dc.description | Plain TeX 18 pages. Version 2; minor changes. To appear on Monatshefte fuer Mathematik | |
| dc.identifier | https://arxiv.org/abs/math/0311030 | |
| dc.identifier | http://arxiv.org/abs/math/0311030 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69057 | |
| dc.subject | Number Theory | |
| dc.subject | 11J25 | |
| dc.title | A lower bound for the height of a rational function at $S$-unit points | |
| dc.type | text |