Geodesic
Variations on the theme of D.\,K.~Faddeev's paper ``An explicit form of the Kummer--Takagi reciprocity law''
Algebra i analiz, Tome 19 (2007) no. 5, pp. 65-69.

Voir la notice de l'article provenant de la source Math-Net.Ru

The following form of the Eisenstein reciprocity law is established: in the cyclotomic field $\mathbb{Q}(\zeta)$, the relation $(\frac{\alpha}{a})=(\frac{a}{\alpha})$ is equivalent to $\frac{a^{p-1}-1}{p}\cdot \underline{\alpha}'(1)\equiv 0\mod p$.
Keywords: Reciprocity law, cyclotomic field. 
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S. V. Vostokov. Variations on the theme of D.\,K.~Faddeev's paper ``An explicit form of the Kummer--Takagi reciprocity law''. Algebra i analiz, Tome 19 (2007) no. 5, pp. 65-69. http://geodesic.mathdoc.fr/item/AA_2007_19_5_a2/

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