Timeline for Naive point count underestimates the number of mod $p$ points of an elliptic curve for infinitely many primes
Current License: CC BY-SA 4.0
9 events
when toggle format | what | by | license | comment | |
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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 |