Artin's Reciprocity Theorem

A general reciprocity theorem for all orders which covered all other known reciprocity theorems when proved by E. Artin in 1927. If R is a number field and R^' a finite integral extension, then there is a surjection from the group of fractional ideals prime to the discriminant, given by the Artin symbol. For some cycle c, the kernel of this surjection contains each principal fractional ideal generated by an element congruent to 1 mod c.

See also

Langlands Program

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Cite this as:

Weisstein, Eric W. "Artin's Reciprocity Theorem." From MathWorld--A Wolfram Web Resource.

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