The class number one problem for the real quadratic fields $\mathbb {Q}(\sqrt {(an)^2+4a})$
Acta Arithmetica, Tome 172 (2016) no. 2, pp. 117-131
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We solve unconditionally the class number one problem for the $2$-parameter family of real quadratic fields ${\mathbb Q}(\sqrt{d})$ with square-free discriminant
$d=(an)^2+4a$ for positive odd integers $a$ and $n$.
Keywords:
solve unconditionally class number problem parameter family real quadratic fields mathbb sqrt square free discriminant positive odd integers
Affiliations des auteurs :
András Biró 1 ; Kostadinka Lapkova 1
@article{10_4064_aa7957_12_2015,
author = {Andr\'as Bir\'o and Kostadinka Lapkova},
title = {The class number one problem for the real quadratic fields $\mathbb {Q}(\sqrt {(an)^2+4a})$},
journal = {Acta Arithmetica},
pages = {117--131},
publisher = {mathdoc},
volume = {172},
number = {2},
year = {2016},
doi = {10.4064/aa7957-12-2015},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa7957-12-2015/}
}
TY - JOUR
AU - András Biró
AU - Kostadinka Lapkova
TI - The class number one problem for the real quadratic fields $\mathbb {Q}(\sqrt {(an)^2+4a})$
JO - Acta Arithmetica
PY - 2016
SP - 117
EP - 131
VL - 172
IS - 2
PB - mathdoc
UR - http://geodesic.mathdoc.fr/articles/10.4064/aa7957-12-2015/
DO - 10.4064/aa7957-12-2015
LA - en
ID - 10_4064_aa7957_12_2015
ER -
%0 Journal Article
%A András Biró
%A Kostadinka Lapkova
%T The class number one problem for the real quadratic fields $\mathbb {Q}(\sqrt {(an)^2+4a})$
%J Acta Arithmetica
%D 2016
%P 117-131
%V 172
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa7957-12-2015/
%R 10.4064/aa7957-12-2015
%G en
%F 10_4064_aa7957_12_2015
András Biró; Kostadinka Lapkova. The class number one problem for the real quadratic fields $\mathbb {Q}(\sqrt {(an)^2+4a})$. Acta Arithmetica, Tome 172 (2016) no. 2, pp. 117-131. doi: 10.4064/aa7957-12-2015
Cité par Sources :