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- W1569595334 abstract "Let E be an elliptic curve over the rationals without complex multiplication. The absolute Galois group of Q acts on the group of torsion points of E, and this action can be expressed in terms of a Galois representation rho_E:Gal(Qbar/Q) to GL_2(Zhat). A renowned theorem of Serre says that the image of rho_E is open, and hence has finite index, in GL_2(Zhat). We give the first general bounds of this index in terms of basic invariants of E. For example, the index can be bounded by a polynomial function of the logarithmic height of the j-invariant of E. As an application of our bounds, we settle an open question on the average of constants arising from the Lang-Trotter conjecture." @default.
- W1569595334 created "2016-06-24" @default.
- W1569595334 creator A5013166421 @default.
- W1569595334 date "2011-02-23" @default.
- W1569595334 modified "2023-09-27" @default.
- W1569595334 title "Bounds for Serre's open image theorem" @default.
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