Geodesic
On a problem in simultaneous Diophantine approximation: Schmidt’s conjecture
Dzmitry Badziahin1 ; Andrew Pollington2 ; Sanju Velani3
1 Department of Mathematics<br/>University of York<br/>Heslington<br/> York YO10 5DD <br/>United Kingdom
2 Division of Mathematical Sciences<br/>National Science Foundation<br/> Arlington, VA 22230
3 Department of Mathematics<br/>University of York<br/>Heslington<br/> York YO10 5DD<br/>United Kingdom
Annals of mathematics, Tome 174 (2011) no. 3, pp. 1837-1883.

Voir la notice de l'article provenant de la source Annals of Mathematics website

For any $i,j \ge 0$ with $i+j =1$, let $\mathbf{Bad}(i,j)$ denote the set of points $(x,y) \in \mathbb{R}^2$ for which $ \max \{ \|qx\|^{1/i}, \, \|qy\|^{1/j} \} > c/q $ for all $ q \in \mathbb{N}$. Here $c = c(x,y)$ is a positive constant. Our main result implies that any finite intersection of such sets has full dimension. This settles a conjecture of Wolfgang M. Schmidt in the theory of simultaneous Diophantine approximation.
DOI : 10.4007/annals.2011.174.3.9

Dzmitry Badziahin 1 ; Andrew Pollington 2 ; Sanju Velani 3

1 Department of Mathematics<br/>University of York<br/>Heslington<br/> York YO10 5DD <br/>United Kingdom
2 Division of Mathematical Sciences<br/>National Science Foundation<br/> Arlington, VA 22230
3 Department of Mathematics<br/>University of York<br/>Heslington<br/> York YO10 5DD<br/>United Kingdom 
@article{10_4007_annals_2011_174_3_9,
     author = {Dzmitry Badziahin and Andrew Pollington and Sanju Velani},
     title = {On a problem in simultaneous {Diophantine} approximation: {Schmidt{\textquoteright}s} conjecture},
     journal = {Annals of mathematics},
     pages = {1837--1883},
     publisher = {mathdoc},
     volume = {174},
     number = {3},
     year = {2011},
     doi = {10.4007/annals.2011.174.3.9},
     mrnumber = {2846492},
     zbl = {06005485},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.174.3.9/}
}
TY  - JOUR
AU  - Dzmitry Badziahin
AU  - Andrew Pollington
AU  - Sanju Velani
TI  - On a problem in simultaneous Diophantine approximation: Schmidt’s conjecture
JO  - Annals of mathematics
PY  - 2011
SP  - 1837
EP  - 1883
VL  - 174
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.174.3.9/
DO  - 10.4007/annals.2011.174.3.9
LA  - en
ID  - 10_4007_annals_2011_174_3_9
ER  - 
%0 Journal Article
%A Dzmitry Badziahin
%A Andrew Pollington
%A Sanju Velani
%T On a problem in simultaneous Diophantine approximation: Schmidt’s conjecture
%J Annals of mathematics
%D 2011
%P 1837-1883
%V 174
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.174.3.9/
%R 10.4007/annals.2011.174.3.9
%G en
%F 10_4007_annals_2011_174_3_9
Dzmitry Badziahin; Andrew Pollington; Sanju Velani. On a problem in simultaneous Diophantine approximation: Schmidt’s conjecture. Annals of mathematics, Tome 174 (2011) no. 3, pp. 1837-1883. doi : 10.4007/annals.2011.174.3.9. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.174.3.9/

Cité par Sources :