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Jan 15, 2020 at 13:28 comment added Will Sawin @vzn Sure, but we're talking about using decades of work in one of the most technically difficult fields of mathematics to avoid about a page of reasoning that's been understood for decades before that.
Jan 15, 2020 at 4:39 comment added user145520 @WillSawin but I suppose you would agree that it follows more immediately from Sato-Tate than from modularity.
Jan 14, 2020 at 18:49 answer added Frob p timeline score: 4
Jan 14, 2020 at 18:20 comment added Will Sawin I just want to point out that one only needs the modularity theorem here, not the (much more difficult) Sato-Tate conjecture.
Jan 13, 2020 at 23:48 comment added user145520 @GerryMyerson strictly speaking $n_p$ is not defined for primes dividing $N$. One could take Neron models or something like that but I would prefer not to invoke anything non-trivial unless necessary (and as you point out it is not necessary here).
Jan 13, 2020 at 20:21 comment added Dror Speiser I will venture a guess: without modularity, no, one cannot show it. The question is closely related to the continuation of the L-series to the point 1, and I think there was no progress on this until modularity (where for CM forms we count the earlier modularity result)
Jan 13, 2020 at 19:01 answer added Asvin timeline score: 4
Jan 13, 2020 at 14:46 comment added Gerry Myerson "not dividing $N$" seems to be an unnecessary condition, as there are only finitely many primes dividing $N$.
Jan 13, 2020 at 5:45 history asked user145520 CC BY-SA 4.0