Timeline for What is the automorphic interpretation of the Weil conjectures over finite fields
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 25, 2018 at 23:38 | comment | added | Asvin | @brunault thanks for confirming, that's great! | |
| Oct 25, 2018 at 18:54 | comment | added | François Brunault | @Asvin For newforms we know the product of eigenvalues of Frobenius, so the bound on the trace is equivalent to the statement on the absolute values of the eigenvalues. For general automorphic forms the generalized Ramanujan conjecture is about the absolute values of the eigenvalues. | |
| Oct 25, 2018 at 9:23 | history | edited | Daniel Loughran | CC BY-SA 4.0 |
added 465 characters in body
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| Oct 24, 2018 at 21:19 | comment | added | Asvin | Right, but that is because we already know the discriminant. Maybe the two are equivalent on general but I don't know... | |
| Oct 24, 2018 at 21:19 | comment | added | Daniel Loughran | I'm not sure about in general, but at least in the case of curves, the Hasse-Weil bound $|C(\mathbb{F}_p) - p +1| \leq 2g \sqrt{p}$ is equivalent to the Riemann hypothesis for the zeta function (see en.wikipedia.org/wiki/Hasse%27s_theorem_on_elliptic_curves). | |
| Oct 24, 2018 at 21:03 | comment | added | Asvin | Also i edited in a third question (which i think you partially answer in your answer to the second question). | |
| Oct 24, 2018 at 20:36 | comment | added | Asvin | Thanks, this is along the lines of what I was thinking. However, doesn't the ramanujan conjecture seem weaker than the statement that the roots have a prescribed absolute value bound? As far as I know, the ramanujan conjecture only seems to bound the trace (I only know the modular form case...) | |
| Oct 24, 2018 at 16:25 | history | answered | Daniel Loughran | CC BY-SA 4.0 |