# Linear equations over multiplicative groups, recurrences, and mixing I

@article{Derksen2010LinearEO, title={Linear equations over multiplicative groups, recurrences, and mixing I}, author={Harm Derksen and David Masser}, journal={Proceedings of the London Mathematical Society}, year={2010}, volume={104} }

Let K be a field of positive characteristic. When V is a linear variety in Kn and G is a finitely generated subgroup of K*, we show how to compute the set V∩Gn 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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