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Thue equations and CM-fields

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Abstract

We obtain a polynomial-type upper bounds for the size and the number of the integral solutions of Thue equations \(F(X,Y) = b\) defined over a totally real number field K, assuming that F(X, 1) has a root \(\alpha \) such that \(K(\alpha )\) is a CM-field. Furthermore, we give an algorithm for the computation of the integral solutions of such an equation.

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Acknowledgments

This work was done during the visit of the second author at the Department of Mathematics of the University of Toulon. The second author wants to thank the department for its warm hospitality and fruitful collaboration. The authors would also like to thank Stéphane Louboutin and Kalman Győry for fruitful discussions.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulon, Université de Toulon, France and Insitut de Mathématiques de Marseille, CNRS-UMR 7373, Aix-Marseille Université, Marseille, France

    Yves Aubry

  2. Department of Mathematics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    Dimitrios Poulakis

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  1. Yves Aubry
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  2. Dimitrios Poulakis
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Correspondence to Dimitrios Poulakis.

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Aubry, Y., Poulakis, D. Thue equations and CM-fields. Ramanujan J 42, 145–156 (2017). https://doi.org/10.1007/s11139-015-9749-x

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  • DOI: https://doi.org/10.1007/s11139-015-9749-x

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