Effective approximation and Diophantine applications
Acta Arithmetica, Tome 177 (2017) no. 2, pp. 169-199
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
using thue siegel method obtain effective improvements liouville irrationality measure certain one parameter families algebraic numbers defined equations type t a apply these corresponding diophantine equations obtain bounds size solutions which depend polynomially bounds number these solutions which independent cases even independent degree equation
Affiliations des auteurs :
Gabriel A. Dill 1
Gabriel A. Dill. Effective approximation and Diophantine applications. Acta Arithmetica, Tome 177 (2017) no. 2, pp. 169-199. doi: 10.4064/aa8430-9-2016
@article{10_4064_aa8430_9_2016,
author = {Gabriel A. Dill},
title = {Effective approximation and {Diophantine} applications},
journal = {Acta Arithmetica},
pages = {169--199},
year = {2017},
volume = {177},
number = {2},
doi = {10.4064/aa8430-9-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8430-9-2016/}
}
Cité par Sources :