On the Surjectivity of the Galois Representations Associated to Non-CM Elliptic Curves
Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 16-31
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Let $E$ be an elliptic curve defined over $\mathbb{Q}$ , of conductor $N$ and without complex multiplication. For any positive integer $l$ , let ${{\phi }_{1}}$ be the Galois representation associated to the $l$ -division points of $E$ . From a celebrated 1972 result of Serre we know that ${{\phi }_{1}}$ 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 ${{\phi }_{1}}$ is not surjective.
Cojocaru, Alina Carmen; Kani, Ernst. On the Surjectivity of the Galois Representations Associated to Non-CM Elliptic Curves. Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 16-31. doi: 10.4153/CMB-2005-002-x
@article{10_4153_CMB_2005_002_x,
author = {Cojocaru, Alina Carmen and Kani, Ernst},
title = {On the {Surjectivity} of the {Galois} {Representations} {Associated} to {Non-CM} {Elliptic} {Curves}},
journal = {Canadian mathematical bulletin},
pages = {16--31},
year = {2005},
volume = {48},
number = {1},
doi = {10.4153/CMB-2005-002-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-002-x/}
}
TY - JOUR AU - Cojocaru, Alina Carmen AU - Kani, Ernst TI - On the Surjectivity of the Galois Representations Associated to Non-CM Elliptic Curves JO - Canadian mathematical bulletin PY - 2005 SP - 16 EP - 31 VL - 48 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-002-x/ DO - 10.4153/CMB-2005-002-x ID - 10_4153_CMB_2005_002_x ER -
%0 Journal Article %A Cojocaru, Alina Carmen %A Kani, Ernst %T On the Surjectivity of the Galois Representations Associated to Non-CM Elliptic Curves %J Canadian mathematical bulletin %D 2005 %P 16-31 %V 48 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-002-x/ %R 10.4153/CMB-2005-002-x %F 10_4153_CMB_2005_002_x
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