Let $p$ and $q$ be distinct primes such that $p \equiv q \pmod{4}$
and consider the quadratic field $K = \mathbf{Q}(\sqrt{pq})$.
In this paper, we shall investigate the class group and
determine the exact power of 2 dividing the class number of
$K$ using the theory of ideals and a theorem on the solvability
of $ax^2 + by^2 = z^2$.
Publié le : 2004-02-14
Classification:
Quadratic fields,
class number,
residue characters,
11R29,
11R11
@article{1116442123,
author = {Nemenzo, Fidel R.},
title = {On a theorem of Scholz on the class number of quadratic fields},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {80},
number = {6},
year = {2004},
pages = { 9-11},
language = {en},
url = {http://dml.mathdoc.fr/item/1116442123}
}
Nemenzo, Fidel R. On a theorem of Scholz on the class number of quadratic fields. Proc. Japan Acad. Ser. A Math. Sci., Tome 80 (2004) no. 6, pp. 9-11. http://gdmltest.u-ga.fr/item/1116442123/