Eisenstein Reciprocity
Suppose that ζ is an th root of unity for some odd prime . The power character is the power of ζ such that
for any prime ideal of Z. It is extended to other ideals by multiplicativity. The Eisenstein reciprocity law states that
for a any rational integer coprime to and α any element of Z that is coprime to a and and congruent to a rational integer modulo (1–ζ)2.
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