A generalization of Scholz’s reciprocity law
Journal de Théorie des Nombres de Bordeaux, Tome 19 (2007) no. 3, pp. 583-594.

Nous donnons une généralisation de la loi de réciprocité de Scholz fondée sur les sous-corps K 2 t-1 et K 2 t de (ζ p ) de degrés 2 t-1 et 2 t sur , respectivement. La démonstration utilise un choix particulier d’élément primitif pour K 2 t sur K 2 t-1 et est basée sur la division du polynôme cyclotomique Φ p (x) sur les sous-corps.

We provide a generalization of Scholz’s reciprocity law using the subfields K 2 t-1 and K 2 t of (ζ p ), of degrees 2 t-1 and 2 t over , respectively. The proof requires a particular choice of primitive element for K 2 t over K 2 t-1 and is based upon the splitting of the cyclotomic polynomial Φ p (x) over the subfields.

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DOI : https://doi.org/10.5802/jtnb.604
@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},
     zbl = {1209.11092},
     mrnumber = {2388790},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.604/}
}
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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