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Stickelberger Relation


Let P be a prime ideal in D_m not containing m. Then

 (Phi(P))=P^(sumtsigma_t^(-1)),

where the sum is over all 1<=t<m which are relatively prime to m. Here D_m is the ring of integers in Q(zeta_m), Phi(P)=g(P)^m, and other quantities are defined by Ireland and Rosen (1990).


See also

Prime Ideal

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References

Ireland, K. and Rosen, M. "The Stickelberger Relation and the Eisenstein Reciprocity Law." Ch. 14 in A Classical Introduction to Modern Number Theory, 2nd ed. New York: Springer-Verlag, pp. 203-227, 1990.

Referenced on Wolfram|Alpha

Stickelberger Relation

Cite this as:

Weisstein, Eric W. "Stickelberger Relation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StickelbergerRelation.html

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