Nous donnons une généralisation de la loi de réciprocité de Scholz fondée sur les sous-corps et de de degrés et sur , respectivement. La démonstration utilise un choix particulier d’élément primitif pour sur et est basée sur la division du polynôme cyclotomique sur les sous-corps.
We provide a generalization of Scholz’s reciprocity law using the subfields and of , of degrees and over , respectively. The proof requires a particular choice of primitive element for over and is based upon the splitting of the cyclotomic polynomial over the subfields.
@article{JTNB_2007__19_3_583_0, author = {Mark Budden and Jeremiah Eisenmenger and Jonathan Kish}, title = {A generalization of {Scholz{\textquoteright}s} reciprocity law}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {583--594}, publisher = {Universit\'e Bordeaux 1}, volume = {19}, number = {3}, year = {2007}, doi = {10.5802/jtnb.604}, mrnumber = {2388790}, zbl = {1209.11092}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.604/} }
TY - JOUR AU - Mark Budden AU - Jeremiah Eisenmenger AU - Jonathan Kish TI - A generalization of Scholz’s reciprocity law JO - Journal de théorie des nombres de Bordeaux PY - 2007 SP - 583 EP - 594 VL - 19 IS - 3 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.604/ DO - 10.5802/jtnb.604 LA - en ID - JTNB_2007__19_3_583_0 ER -
%0 Journal Article %A Mark Budden %A Jeremiah Eisenmenger %A Jonathan Kish %T A generalization of Scholz’s reciprocity law %J Journal de théorie des nombres de Bordeaux %D 2007 %P 583-594 %V 19 %N 3 %I Université Bordeaux 1 %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.604/ %R 10.5802/jtnb.604 %G en %F JTNB_2007__19_3_583_0
Mark Budden; Jeremiah Eisenmenger; Jonathan Kish. A generalization of Scholz’s reciprocity law. Journal de théorie des nombres de Bordeaux, Tome 19 (2007) no. 3, pp. 583-594. doi : 10.5802/jtnb.604. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.604/
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