Thue equations and CM-fields

Yves Aubry; Dimitrios Poulakis

Thue equations and CM-fields

Number Theory 2015-01-08 v4

Authors: Yves Aubry , Dimitrios Poulakis

Abstract

We obtain a polynomial type upper bound for the size 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.

Keywords

polynomial theory upper bounds

Cite

@article{arxiv.1407.6556,
  title  = {Thue equations and CM-fields},
  author = {Yves Aubry and Dimitrios Poulakis},
  journal= {arXiv preprint arXiv:1407.6556},
  year   = {2015}
}

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