Geodesic
Congruent numbers over real number fields
Tomasz Jędrzejak1
1 Institute of Mathematics University of Szczecin Wielkopolska 15 70-451 Szczecin, Poland
Colloquium Mathematicum, Tome 128 (2012) no. 2, pp. 179-186.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

It is classical that a natural number $n$ is congruent iff the rank of $\mathbb{Q}$-points on $E_{n}:y^{2}=x^{3}-n^{2}x$ is positive. In this paper, following Tada (2001), we consider generalised congruent numbers. We extend the above classical criterion to several infinite families of real number fields.
DOI : 10.4064/cm128-2-3
Keywords: classical natural number congruent rank mathbb points n positive paper following tada consider generalised congruent numbers extend above classical criterion several infinite families real number fields

Tomasz Jędrzejak 1

1 Institute of Mathematics University of Szczecin Wielkopolska 15 70-451 Szczecin, Poland 
@article{10_4064_cm128_2_3,
     author = {Tomasz J\k{e}drzejak},
     title = {Congruent numbers over real number fields},
     journal = {Colloquium Mathematicum},
     pages = {179--186},
     publisher = {mathdoc},
     volume = {128},
     number = {2},
     year = {2012},
     doi = {10.4064/cm128-2-3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm128-2-3/}
}
TY  - JOUR
AU  - Tomasz Jędrzejak
TI  - Congruent numbers over real number fields
JO  - Colloquium Mathematicum
PY  - 2012
SP  - 179
EP  - 186
VL  - 128
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm128-2-3/
DO  - 10.4064/cm128-2-3
LA  - en
ID  - 10_4064_cm128_2_3
ER  - 
%0 Journal Article
%A Tomasz Jędrzejak
%T Congruent numbers over real number fields
%J Colloquium Mathematicum
%D 2012
%P 179-186
%V 128
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm128-2-3/
%R 10.4064/cm128-2-3
%G en
%F 10_4064_cm128_2_3
Tomasz Jędrzejak. Congruent numbers over real number fields. Colloquium Mathematicum, Tome 128 (2012) no. 2, pp. 179-186. doi : 10.4064/cm128-2-3. http://geodesic.mathdoc.fr/articles/10.4064/cm128-2-3/

Cité par Sources :