On a paper of Hasse concerning the Eisenstein reciprocity law

S. V. Vostokov, M. A. Ivanov, G. K. Pak

Research output: Contribution to journalArticlepeer-review

Abstract

In the present paper, necessary and sufficient conditions are given for the equality of the power residue symbols ${\left( {\frac{\alpha }{a}} \right)_n} $ and $ {\left( {\frac{a}{\alpha}} \right)_n} $ in the cyclotomic field $\Bbb Q(\zeta _n)$, $2\nmid n$, for $a \in \Bbb Z, (a,n) = 1$. This result is a generalization of the classical Eisenstein reciprocity law and its continuation in Hasse's paper
Original languageEnglish
Pages (from-to)525-529
JournalJournal of Mathematical Sciences
Volume161
Issue number4
DOIs
StatePublished - 2009

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