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$\DeclareMathOperator\Frob{Frob}$Iwaniec and Kowalski, in their famous book Analytic Number Theory states a strong form of the effective Chebotarev density theorem page 143, and prove it assuming both ...

If $E$ is a non-CM elliptic curve over $Q$, then it is a famous theorem of Serre that there is some integer $M(E)$ such that for any prime $\ell > M(E)$, the image of the Galois representations $\...

Edit: as GH noticed, the way I tried to state Montgomery's conjecture is wrong. There were some mistakes in the references I used, which compounded with some mistakes of mine, gave a very poor post. ...