TY - JOUR

T1 - On a paper of Hasse concerning the Eisenstein reciprocity law

AU - Vostokov, S. V.

AU - Ivanov, M. A.

AU - Pak, G. K.

PY - 2009

Y1 - 2009

N2 - 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

AB - 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

U2 - 10.1007/s10958-009-9580-2

DO - 10.1007/s10958-009-9580-2

M3 - Article

VL - 161

SP - 525

EP - 529

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -