It is classical that a natural number n is congruent iff the rank of ℚ -points on Eₙ: y² = x³-n²x 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-3,
author = {Tomasz J\k edrzejak},
title = {Congruent numbers over real number fields},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {179-186},
zbl = {1290.11095},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-3}
}
Tomasz Jędrzejak. Congruent numbers over real number fields. Colloquium Mathematicae, Tome 126 (2012) pp. 179-186. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm128-2-3/