Title: ON THE DENSITY OF DISCRIMINANTS OF ABELIAN EXTENSIONS OF A NUMBER FIELD
Abstract: Let G = C ℓ × C ℓ 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≤X N(k, G; m). This extends the result previously obtained by Datskovsky and Mammo.
Publication Year: 2010
Publication Date: 2010-09-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 1
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot