Abstract
To each nontotally real cubic extension K of Q and to each generator α of the cubic field K, we attach a family of cubic Thue equations, indexed by the units of K, and we prove that this family of cubic Thue equations has only a finite number of integer solutions, by giving an effective upper bound for these solutions.
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Notes
- 1.
The lower bound follows from looking at the norm!
References
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Levesque, C., Waldschmidt, M. (2013). Families of Cubic Thue Equations with Effective Bounds for the Solutions. In: Borwein, J., Shparlinski, I., Zudilin, W. (eds) Number Theory and Related Fields. Springer Proceedings in Mathematics & Statistics, vol 43. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6642-0_12
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DOI: https://doi.org/10.1007/978-1-4614-6642-0_12
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