Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593315 | Journal of Number Theory | 2016 | 27 Pages |
Abstract
Let K be a number field and let E1,…,EnE1,…,En be elliptic curves over K , pairwise non-isogenous over K‾ and without complex multiplication over K‾. We study the image G∞G∞ of the adelic representation of Gal(K‾/K) naturally attached to E1×⋯×EnE1×⋯×En. The main result is an explicit bound for the index of G∞G∞ in {(x1,…,xn)∈GL2(Zˆ)n|detxi=detxj∀i,j}.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Davide Lombardo,