Binary quadratic forms and Eichler orders

Alsina, Montserrat. "Binary quadratic forms and Eichler orders." Journal de Théorie des Nombres de Bordeaux 17.1 (2005): 13-23. <http://eudml.org/doc/249437>.

@article{Alsina2005,
abstract = {For any Eichler order $\mathcal\{O\}(D,N)$ of level $N$ in an indefinite quaternion algebra of discriminant $D$ there is a Fuchsian group $\Gamma (D,N)\subseteq \operatorname\{SL\}(2,\mathbb\{R\})$ and a Shimura curve $X(D,N)$. We associate to $\mathcal\{O\}(D,N)$ a set $\mathcal\{H\}(\mathcal\{O\}(D,N))$ of binary quadratic forms which have semi-integer quadratic coefficients, and we develop a classification theory, with respect to $\Gamma (D,N)$, for primitive forms contained in $\mathcal\{H\}(\mathcal\{O\}(D,N))$. In particular, the classification theory of primitive integral binary quadratic forms by $\operatorname\{SL\}(2,\mathbb\{Z\})$ is recovered. Explicit fundamental domains for $\Gamma (D,N)$ allow the characterization of the $\Gamma (D,N)$-reduced forms.},
affiliation = {Dept. Matemàtica Aplicada III EUPM Av. Bases de Manresa 61-73, Manresa-08240, Catalunya, Spain},
author = {Alsina, Montserrat},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {1},
pages = {13-23},
publisher = {Université Bordeaux 1},
title = {Binary quadratic forms and Eichler orders},
url = {http://eudml.org/doc/249437},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Alsina, Montserrat
TI - Binary quadratic forms and Eichler orders
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 1
SP - 13
EP - 23
AB - For any Eichler order $\mathcal{O}(D,N)$ of level $N$ in an indefinite quaternion algebra of discriminant $D$ there is a Fuchsian group $\Gamma (D,N)\subseteq \operatorname{SL}(2,\mathbb{R})$ and a Shimura curve $X(D,N)$. We associate to $\mathcal{O}(D,N)$ a set $\mathcal{H}(\mathcal{O}(D,N))$ of binary quadratic forms which have semi-integer quadratic coefficients, and we develop a classification theory, with respect to $\Gamma (D,N)$, for primitive forms contained in $\mathcal{H}(\mathcal{O}(D,N))$. In particular, the classification theory of primitive integral binary quadratic forms by $\operatorname{SL}(2,\mathbb{Z})$ is recovered. Explicit fundamental domains for $\Gamma (D,N)$ allow the characterization of the $\Gamma (D,N)$-reduced forms.
LA - eng
UR - http://eudml.org/doc/249437
ER -