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Effective approximation and Diophantine applications

Dill, Gabriel. (2016) Effective approximation and Diophantine applications. Preprints Fachbereich Mathematik, 2016 (09).

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Abstract

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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Zahlentheorie (Habegger)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Dill, Gabriel
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:21 Apr 2019 22:36
Deposited On:28 Mar 2019 09:51

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