Geodesic
Effective approximation and Diophantine applications
Gabriel A. Dill1
1 Departement Mathematik und Informatik Universität Basel Spiegelgasse 1 CH-4051 Basel, Switzerland
Acta Arithmetica, Tome 177 (2017) no. 2, pp. 169-199 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/aa8430-9-2016
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

Gabriel A. Dill 1

1 Departement Mathematik und Informatik Universität Basel Spiegelgasse 1 CH-4051 Basel, Switzerland 
@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/}
}
TY  - JOUR
AU  - Gabriel A. Dill
TI  - Effective approximation and Diophantine applications
JO  - Acta Arithmetica
PY  - 2017
SP  - 169
EP  - 199
VL  - 177
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa8430-9-2016/
DO  - 10.4064/aa8430-9-2016
LA  - en
ID  - 10_4064_aa8430_9_2016
ER  - 
%0 Journal Article
%A Gabriel A. Dill
%T Effective approximation and Diophantine applications
%J Acta Arithmetica
%D 2017
%P 169-199
%V 177
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/aa8430-9-2016/
%R 10.4064/aa8430-9-2016
%G en
%F 10_4064_aa8430_9_2016
Gabriel A. Dill. Effective approximation and Diophantine applications. Acta Arithmetica, Tome 177 (2017) no. 2, pp. 169-199. doi: 10.4064/aa8430-9-2016

Cité par Sources :