Geodesic
On the negative Pell equation
Étienne Fouvry1 ; Jürgen Klüners2
1 Université Paris-Sud<br/>Laboratoire de mathématique, UMR 8628<br/>CNRS, F-91405 Orsay Cedex<br/>France
2 Universität Paderborn<br/>Institut für Mathematik<br/>33095 Paderborn<br/>Germany
Annals of mathematics, Tome 172 (2010) no. 3, pp. 2035-2104.

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

We give asymptotic upper and lower bounds for the number of squarefree $d$ ($0\lt d\leq X$) such that the equation $x^2-dy^2=-1$ is solvable. These estimates, as usual, can equivalently be interpreted in terms of real quadratic fields with a fundamental unit with norm $-1$ and give strong evidence in the direction of a conjecture due to P. Stevenhagen.
DOI : 10.4007/annals.2010.172.2035

Étienne Fouvry 1 ; Jürgen Klüners 2

1 Université Paris-Sud<br/>Laboratoire de mathématique, UMR 8628<br/>CNRS, F-91405 Orsay Cedex<br/>France
2 Universität Paderborn<br/>Institut für Mathematik<br/>33095 Paderborn<br/>Germany 
@article{10_4007_annals_2010_172_2035,
     author = {\'Etienne Fouvry and J\"urgen Kl\"uners},
     title = {On the negative {Pell} equation},
     journal = {Annals of mathematics},
     pages = {2035--2104},
     publisher = {mathdoc},
     volume = {172},
     number = {3},
     year = {2010},
     doi = {10.4007/annals.2010.172.2035},
     mrnumber = {2726105},
     zbl = {05850192},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.2035/}
}
TY  - JOUR
AU  - Étienne Fouvry
AU  - Jürgen Klüners
TI  - On the negative Pell equation
JO  - Annals of mathematics
PY  - 2010
SP  - 2035
EP  - 2104
VL  - 172
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.2035/
DO  - 10.4007/annals.2010.172.2035
LA  - en
ID  - 10_4007_annals_2010_172_2035
ER  - 
%0 Journal Article
%A Étienne Fouvry
%A Jürgen Klüners
%T On the negative Pell equation
%J Annals of mathematics
%D 2010
%P 2035-2104
%V 172
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.2035/
%R 10.4007/annals.2010.172.2035
%G en
%F 10_4007_annals_2010_172_2035
Étienne Fouvry; Jürgen Klüners. On the negative Pell equation. Annals of mathematics, Tome 172 (2010) no. 3, pp. 2035-2104. doi : 10.4007/annals.2010.172.2035. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.2035/

Cité par Sources :