Linear equations over multiplicative groups, recurrences, and mixing I

@inproceedings{Derksen2012LinearEO,
  title={Linear equations over multiplicative groups, recurrences, and mixing I},
  author={Harm Derksen and D. W. Masser},
  year={2012}
}
Let K be a field of positive characteristic. When V is a linear variety in K^n and G is a finitely generated subgroup of K^*, we show how to compute the intersection of V and G^n effectively using heights. We calculate all the estimates explicitly. A special case provides the effective solution of the S-unit equation in n variables. 

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