ON THE DENSITY OF DISCRIMINANTS OF ABELIAN EXTENSIONS OF A NUMBER FIELD
2010 ◽
Vol 06
(06)
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pp. 1273-1291
Keyword(s):
Let G = Cℓ × Cℓ denote the product of two cyclic groups of prime order ℓ, and let k be an algebraic number field. Let N(k, G, m) denote the number of abelian extensions K of k with Galois group G(K/k) isomorphic to G, and the relative discriminant 𝒟(K/k) of norm equal to m. In this paper, we derive an asymptotic formula for ∑m≤XN(k, G; m). This extends the result previously obtained by Datskovsky and Mammo.
1961 ◽
Vol 19
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pp. 169-187
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1957 ◽
Vol 12
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pp. 177-189
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1991 ◽
Vol 121
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pp. 161-169
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1984 ◽
Vol 93
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pp. 133-148
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1989 ◽
Vol 115
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pp. 151-164
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1978 ◽
Vol 70
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pp. 183-202
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