Geodesic
On a paper by Hasse concerning Eisenstein reciprocity law
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 18, Tome 365 (2009), pp. 122-129 
S. V. Vostokov; M. A. Ivanov; G. K. Pak. On a paper by Hasse concerning Eisenstein reciprocity law. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 18, Tome 365 (2009), pp. 122-129. http://geodesic.mathdoc.fr/item/ZNSL_2009_365_a4/
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     title = {On a~paper by {Hasse} concerning {Eisenstein} reciprocity law},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the present paper we give necessary and sufficient conditions equality power rezidue symbols $(\frac\alpha a)_n$ and $(\frac a\alpha)_n$ in the cyclotomic field $\mathbb Q(\zeta_n)$, $2\nmid n $, for $a\in\mathbb Z$, $(a,n)=1$. This result is generalization of classical Eisenstein reciprocity law and its continuation in Hasse paper. Bibl. – 3 titles.

[1] G. Eisenstein, “Über ein einfaches Mittel zur Auffindung der höheren Reciprocitätsgesetze und der mit ihnen zu verbindenden Ergänzungssätze”, J. für die reine u. ang. Mathematik, 39 (1850), 351–364. | DOI | Zbl

[2] H. Hasse, “Das Eisensteinsche Reziprozitätsgesetz der $n$-ten Potenzreste”, Math. Ann., 97 (1927), 599–623 | DOI | MR | Zbl

[3] S. V. Vostokov, “Klassicheskii zakon vzaimnosti stepennykh vychetov, kak analog teoremy ob abelevom integrale”, Algebra i analiz, 20:6 (2008), 108–118 | MR