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Effective approximation and Diophantine applications

Volume 177 / 2017

Gabriel A. Dill Acta Arithmetica 177 (2017), 169-199 MSC: Primary 11D41; Secondary 11D45, 11D57, 11J68. DOI: 10.4064/aa8430-9-2016 Published online: 22 December 2016


Using the Thue–Siegel method, we obtain effective improvements on Liouville’s irrationality measure for certain one-parameter families of algebraic numbers, defined by equations of the type $(t-a)Q(t)+P(t)=0$. We apply these to some corresponding Diophantine equations. We obtain bounds for the size of solutions, which depend polynomially on $|a|$, and bounds for the number of these solutions, which are independent of $a$ and in some cases even independent of the degree of the equation.


  • Gabriel A. DillDepartement Mathematik und Informatik
    Universität Basel
    Spiegelgasse 1
    CH-4051 Basel, Switzerland

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