Effective approximation and Diophantine applications

Dill, Gabriel A.. (2017) Effective approximation and Diophantine applications. Acta Arithmetica, 177. pp. 169-199.

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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)
UniBasel Contributors:Dill, Gabriel
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Institute of Mathematics, Polish Academy of Sciences
Note:Publication type according to Uni Basel Research Database: Journal article
Identification Number:
Last Modified:13 Oct 2017 09:54
Deposited On:13 Oct 2017 09:54

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