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- W2952200500 abstract "Let $Gamma$ be a finitely generated subgroup of the multiplicative group $G_m^2(bar{Q})$. Let $p(X,Y),q(X,Y)inbat{Q}$ be two coprime polynomials not both vanishing at $(0,0)$; let $epsilon>0$. We prove that, for all $(u,v)inGamma$ outside a proper Zariski closed subset of $G_m^2$, the height of $p(u,v)/q(u,v)$ verifies $h(p(u,v)/q(u,v))>h(1:p(u,v):q(u,v))-epsilon max(h(uu),h(v))$. 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 $Gamma$." @default.
- W2952200500 created "2019-06-27" @default.
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- W2952200500 date "2003-11-04" @default.
- W2952200500 modified "2023-10-01" @default.
- W2952200500 title "A lower bound for the height of a rational function at $S$-unit points" @default.
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