Generalization of the “stark Unit” for Abelian L-functions with Multiple Zeros
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چکیده
Let K/k be a normal extension of number fields with abelian Galois group G. Suppose there is an infinite place v of k such that the set of nontrival characters χ : G−→C× which are ramified at all infinite places except v is nonempty. Then the corresponding Artin L-functions L(χ, s) have zeros of the first order at s = 0, and if we fix any embedding of the bigger field K to C which extends v then Stark’s conjecture predicts existence of a “unit” ε ∈ Q ⊗Z O K such that for every such χ L(χ, 0) = ∑
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تاریخ انتشار 2008