Linear equations in variables which Lie in a multiplicative group

By Jan-Hendrik Evertse, H. P. Schlickewei, W. Schmidt. 2002

251 citations recorded by the source corpus.

Let K be a field of characteristic 0 and let n be a natural number. Let r be a subgroup of the multiplicative group (K*) n of finite rank r. Given a 1 ,...,a n E K* write A(a 1 ,...,a n , Γ) for the number of solutions x = (x 1 ,..., x n ) ∈ Γ 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 , r) which depends only on the dimension n and on the rank r.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a7fac29d05b89df9eb74d82edd152154291418e7

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In Discrete Mathematics and Combinatorics

1. T. Tucker
2. Dragos Ghioca
3. Harm Derksen
4. Robert L. Benedetto
5. Pär Kurlberg
6. Eric Katz

In Geometry and Topology

1. Robert L. Benedetto
2. T. Tucker
3. Pär Kurlberg
4. Dragos Ghioca
5. Harm Derksen
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8. B. Keller

In Mathematical Physics

1. T. Tucker
2. Robert L. Benedetto
3. Dragos Ghioca
4. Pär Kurlberg
5. Harm Derksen
6. Matthew Baker
7. Jerzy Weyman

Citations in the corpus

• A case of the dynamical Mordell–Lang conjecture (2012, background): “and Schmidt [10] have given a strong quantitative version of the Skolem–Mahler– Lech theorem.”
• A Skolem–Mahler–Lech theorem in positive characteristic and finite automata (2005, background): “, βd) may be given in terms of the number of generators of Γ and d (see [7,5,6]).”