Small Heights in Large Non-Abelian Extensions
Abstract
Let E be an elliptic curve over the rationals. Let L be an infinite Galois extension of the rationals with uniformly bounded local degrees at almost all primes. We will consider the infinite extension L(Etor) of the rationals where we adjoin all coordinates of torsion points of E. In this paper we will prove an effective lower bound for the height of non-zero elements in L(Etor) that are not a root of unity.
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