Let be a number field. In this paper, we give a formula for the mean value of the square of class number times regulator for certain families of quadratic extensions of characterized by finitely many local conditions. We approach this by using the theory of the zeta function associated with the space of pairs of quaternion algebras. We also prove an asymptotic formula of the correlation coefficient for class number times regulator of certain families of quadratic extensions.
Soit un corps de nombres. Dans cet article, nous donnons une formule pour la valeur moyenne du carré du nombre de classe multiplié par le régulateur pour certaines familles d’extensions quadratiques de caractérisées par un nombre fini de conditions locales. Notre approche utilise la théorie de la fonction zêta associée à l’espace de paires d’algèbres de quaternions. Nous prouvons aussi une formule asymptotique pour le coefficient de corrélation du nombre de classe multiplié par le régulateur de certaines familles d’extensions quadratiques.
Keywords: Density theorem, prehomogeneous vector space, quaternion algebra, local zeta function
Mot clés : théorème densité, espace vectoriel préhomogène, fonction zêta local, algèbres de quaternions
@article{AIF_2008__58_2_625_0, author = {Taniguchi, Takashi}, title = {A mean value theorem for the square of class number times regulator of quadratic extensions}, journal = {Annales de l'Institut Fourier}, pages = {625--670}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {2}, year = {2008}, doi = {10.5802/aif.2363}, mrnumber = {2410385}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2363/} }
TY - JOUR AU - Taniguchi, Takashi TI - A mean value theorem for the square of class number times regulator of quadratic extensions JO - Annales de l'Institut Fourier PY - 2008 SP - 625 EP - 670 VL - 58 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2363/ DO - 10.5802/aif.2363 LA - en ID - AIF_2008__58_2_625_0 ER -
%0 Journal Article %A Taniguchi, Takashi %T A mean value theorem for the square of class number times regulator of quadratic extensions %J Annales de l'Institut Fourier %D 2008 %P 625-670 %V 58 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2363/ %R 10.5802/aif.2363 %G en %F AIF_2008__58_2_625_0
Taniguchi, Takashi. A mean value theorem for the square of class number times regulator of quadratic extensions. Annales de l'Institut Fourier, Volume 58 (2008) no. 2, pp. 625-670. doi : 10.5802/aif.2363. http://www.numdam.org/articles/10.5802/aif.2363/
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