# Artin L-functions for abelian extensions of imaginary quadratic fields.

@inproceedings{Johnson2005ArtinLF, title={Artin L-functions for abelian extensions of imaginary quadratic fields.}, author={Jennifer Michelle Johnson}, year={2005} }

Let F be an abelian extension of an imaginary quadratic field K with Galois group G. We form the Galois-equivariant L-function of the motive h(Spec F)(j) where the Tate twists j are negative integers. The leading term in the Taylor expansion at s=0 decomposes over the group algebra Q[G] into a product of Artin L-functions indexed by the characters of G. We construct a motivic element via the Eisenstein symbol and relate the L-value to periods via regulator maps. Working toward the equivariant… CONTINUE READING

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## Iwasawa Theory and Motivic L-functions

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## Advanced Topics in the Arithmetic of Elliptic Curves

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