We propose a definition of sign of imaginary quadratic fields. We give an example of such functions, and use it to define new invariants that are roots of the classical Ramachandra invariants. Also we introduce signed ordinary distributions and compute their signed cohomology by using Anderson's theory of double complex.
Nous proposons une définition du signe pour les corps quadratiques imaginaires. Nous donnons un exemple de telles fonctions et l'utilisons pour définir de nouveaux invariants qui sont racines des invariants de Ramachandra classiques. D'autre part nous introduisons les distributions ordinaires signées et calculons leur cohomologie à l'aide de la theéorie d'Anderson dite du double complexe.
Keywords: sign function, narrow ray class field, Shimura reciprocity law, ordianary $s$-ditributions, Anderson’s resolution, spectrales sequences
Mot clés : fonction signe, corps de rayon restreints, loi de réciprocité de Shimura, $s$-distributions ordinaires, résolution d’Anderson, suites spectrales
@article{AIF_2005__55_3_753_0, author = {Oukhaba, Hassan}, title = {Sign functions of imaginary quadratic fields and applications}, journal = {Annales de l'Institut Fourier}, pages = {753--772}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {3}, year = {2005}, doi = {10.5802/aif.2113}, mrnumber = {2149402}, zbl = {02171524}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2113/} }
TY - JOUR AU - Oukhaba, Hassan TI - Sign functions of imaginary quadratic fields and applications JO - Annales de l'Institut Fourier PY - 2005 SP - 753 EP - 772 VL - 55 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2113/ DO - 10.5802/aif.2113 LA - en ID - AIF_2005__55_3_753_0 ER -
%0 Journal Article %A Oukhaba, Hassan %T Sign functions of imaginary quadratic fields and applications %J Annales de l'Institut Fourier %D 2005 %P 753-772 %V 55 %N 3 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2113/ %R 10.5802/aif.2113 %G en %F AIF_2005__55_3_753_0
Oukhaba, Hassan. Sign functions of imaginary quadratic fields and applications. Annales de l'Institut Fourier, Volume 55 (2005) no. 3, pp. 753-772. doi : 10.5802/aif.2113. http://www.numdam.org/articles/10.5802/aif.2113/
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