Let $K = \mathbf{Q}(\sqrt{m})$ be a real quadratic field, $\mathcal{O}_K$
its ring of integers and $G = \operatorname{Gal}(K/\mathbf{Q})$.
For $\gamma \in H^1(G, \mathcal{O}_K^{\times})$, we associate
a module $M_c/P_c$ for $\gamma = [c]$. It is known that
$M_c/P_c \approx \mathbf{Z}/\Delta_m \mathbf{Z}$ where $\Delta_m = 1$
or 2 and we will determine $\Delta_m$.
Publié le : 2003-10-14
Classification:
Real quadratic field,
fundamental unit,
parity,
continued fractions,
11R11,
11A55,
11A07
@article{1116443712,
author = {Lee, Seok-Min and Ono, Takashi},
title = {On a certain invariant for real quadratic fields},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {79},
number = {3},
year = {2003},
pages = { 119-122},
language = {en},
url = {http://dml.mathdoc.fr/item/1116443712}
}
Lee, Seok-Min; Ono, Takashi. On a certain invariant for real quadratic fields. Proc. Japan Acad. Ser. A Math. Sci., Tome 79 (2003) no. 3, pp. 119-122. http://gdmltest.u-ga.fr/item/1116443712/