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On the Surjectivity of the Galois Representations Associated to Non-CM Elliptic Curves

  Published:2005-03-01
 Printed: Mar 2005
  • Alina Carmen Cojocaru
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Abstract

Let $ E $ be an elliptic curve defined over $\Q,$ of conductor $N$ and without complex multiplication. For any positive integer $l$, let $\phi_l$ be the Galois representation associated to the $l$-division points of~$E$. From a celebrated 1972 result of Serre we know that $\phi_l$ is surjective for any sufficiently large prime $l$. In this paper we find conditional and unconditional upper bounds in terms of $N$ for the primes $l$ for which $\phi_l$ is {\emph{not}} surjective.
MSC Classifications: 11G05, 11N36, 11R45 show english descriptions Elliptic curves over global fields [See also 14H52]
Applications of sieve methods
Density theorems
11G05 - Elliptic curves over global fields [See also 14H52]
11N36 - Applications of sieve methods
11R45 - Density theorems
 

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