Linear equations in variables which lie in a multiplicative group

• 成果类型: Article
• 署名作者: Evertse, JH; Schlickewei, HP; Schmidt, WM
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3062133
• 发表日期: 2002
• 页码: 807-836
• 关键词: recurrence sequences; s-units; number; roots

摘要

Lot K be a field of characteristic 0 and lot n be a natural number. Let Gamma be a subgroup of the multiplicative group (K*)(n) of finite rank r. Given a(1), ..., a(n) is an element of K* write A(a(1), ..., a(n), Gamma) for the number of solutions x = (x(1), ..., x(n)) is an element of Gamma of the equation a(1)x(1) + (...) + a(n)x(n) = 1, such that no proper subsum of a(1)x(1) + (...) + a(n)x(n) vanishes. We derive an explicit upper bound for A (a(1), ..., a(n), Gamma) which depends only on the dimension n and on the rank r.