For any Eichler order of level in an indefinite quaternion algebra of discriminant there is a Fuchsian group and a Shimura curve . We associate to a set of binary quadratic forms which have semi-integer quadratic coefficients, and we develop a classification theory, with respect to , for primitive forms contained in . In particular, the classification theory of primitive integral binary quadratic forms by is recovered. Explicit fundamental domains for allow the characterization of the -reduced forms.
Pour tout ordre d’Eichler de niveau dans une algèbre de quaternions indéfinie de discriminant , il existe un groupe Fuchsien et une courbe de Shimura . Nous associons à un ensemble de formes quadratiques binaires ayant des coefficients semi-entiers quadratiques et developpons une classification des formes quadratiques primitives de pour rapport à . En particulier nous retrouvons la classification des formes quadratiques primitives et entières de . Un domaine fondamental explicite pour permet de caractériser les formes réduites.
@article{JTNB_2005__17_1_13_0, author = {Alsina, Montserrat}, title = {Binary quadratic forms and {Eichler} orders}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {13--23}, publisher = {Universit\'e Bordeaux 1}, volume = {17}, number = {1}, year = {2005}, doi = {10.5802/jtnb.473}, zbl = {1079.11022}, mrnumber = {2152207}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jtnb.473/} }
TY - JOUR AU - Alsina, Montserrat TI - Binary quadratic forms and Eichler orders JO - Journal de théorie des nombres de Bordeaux PY - 2005 SP - 13 EP - 23 VL - 17 IS - 1 PB - Université Bordeaux 1 UR - http://www.numdam.org/articles/10.5802/jtnb.473/ DO - 10.5802/jtnb.473 LA - en ID - JTNB_2005__17_1_13_0 ER -
Alsina, Montserrat. Binary quadratic forms and Eichler orders. Journal de théorie des nombres de Bordeaux, Volume 17 (2005) no. 1, pp. 13-23. doi : 10.5802/jtnb.473. http://www.numdam.org/articles/10.5802/jtnb.473/
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