Linear equations over multiplicative groups, recurrences, and mixing I

@article{Derksen2012LinearEO,
  title={Linear equations over multiplicative groups, recurrences, and mixing I},
  author={H. Derksen and D. Masser},
  journal={Proceedings of The London Mathematical Society},
  year={2012},
  volume={104},
  pages={1045-1083}
}
Let u1,…,umu1,…,um be linear recurrences with values in a field KK of positive characteristic pp. We show that the set of integer vectors (k1,…,km)(k1,…,km) such that u1(k1)+⋯+um(km)=0u1(k1)+⋯+um(km)=0 is pp-normal in a natural sense generalizing that of the first author, who proved the result for m=1m=1. Furthermore the set is effectively computable if KK is. We illustrate this with an example for m=4m=4. We also show that the corresponding set for zero characteristic is not decidable for m… Expand
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References

SHOWING 1-10 OF 67 REFERENCES
On vanishing coefficients of algebraic power series over fields of positive characteristic
  • 29
  • PDF
Linear equations in variables which Lie in a multiplicative group
  • 190
  • PDF
Inequalities for Heights Of Algebraic Subspaces And the Thue-Siegel Principle
  • 24
Uniformly counting points of bounded height
  • 39
  • PDF
Universal Diophantine Equation
  • J. P. Jones
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 1982
  • 84
...
1
2
3
4
5
...