Author: Lajos Hajdu
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  • 1 University of Debrecen Institute of Mathematics Debrecen Hungary
  • 2 Hungarian Academy of Sciences and University of Debrecen Number Theory Research Group H-4010 Debrecen P.O. Box 12 Hungary
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Abstract  

We show that a particular parameter plays a vital role in the resolution of S-unit equations, at the stage where LLL-reduction is applied. We define the notion of optimal system of fundamental S-units (with respect to this parameter), and prove that such a system exists and can be effectively constructed. Applying our results and methods, one can obtain much better bounds for the solutions of S-unit equations after the reduction step, than earlier. We also briefly discuss some effects of our results on the method of Wildanger and Smart for the resolution of S-unit equations.

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