Linear equations in variables which lie in a multiplicative group

dc.creatorEvertse, J. -H.
dc.creatorSchlickewei, H. P.
dc.creatorSchmidt, W. M.
dc.date2004-09-30
dc.date.accessioned2026-07-07T05:12:45Z
dc.date.available2026-07-07T05:12:45Z
dc.descriptionLet K be a field of characteristic 0 and let n be a natural number. Let Gamma be a subgroup of the multiplicative group $(K^\ast)^n$ of finite rank r. Given $A_2,...,a_n\in K^\ast$ write $A(a_1,...,a_n,Γ)$ for the number of solutions x=(x_1,...,x_n)\in Γ$ of the equation a_1x_1+...+a_nx_n=1$, such that no proper subsum of $a_1x_1+...+a_nx_n$ vanishes. We derive an explicit upper bound for $A(a_1,...,a_n,Γ)$ which depends only on the dimension n and on the rank r.
dc.identifierhttps://arxiv.org/abs/math/0409604
dc.identifierhttp://arxiv.org/abs/math/0409604
dc.identifierAnn. of Math. (2), Vol. 155 (2002), no. 3, 807--836
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72695
dc.subjectNumber Theory
dc.titleLinear equations in variables which lie in a multiplicative group
dc.typetext

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