Timeline for Potential modularity and the Ramanujan conjecture
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 28, 2018 at 16:16 | comment | added | student | I'm sorry you feel that way. But given the (honestly confusing) level of hostility in all of your comments, maybe it's for the best. | |
| Dec 28, 2018 at 9:54 | comment | added | Victor Protsak | In spite of the disqualifying disclaimer, I think that the reference you have included was relevant to the question. However, the rest of your answer was vague, and my comments were constructive. Perhaps OP already knows the answer to his question, but other people may not. It certainly requires time and some degree of expertise to extract the assumptions under which the Ramanujan conjecture is proved in the paper: e.g. weight 2 modular forms are not mentioned anywhere. Now, if you'll excuse me, I will decline to further respond to what increasingly looks like anonymous trolling. | |
| Dec 28, 2018 at 6:11 | comment | added | student | @VictorProtsak, I am still baffled by your comments. I'm sure the OP knows what the Ramanujan conjecture for GL(2) is. Given the question is about deducing Ramanujan from automorphy of symmetric powers and this is exactly what the linked paper claims to do for the CM analog of weight two forms, I find your comments perplexing. But I think we are talking at cross purposes. It feels like you are complaining about something (I'm not sure), but perhaps you are just trying to add clarifying remarks. | |
| Dec 28, 2018 at 5:38 | comment | added | Victor Protsak | For $F=\Bbb{Q}$, the Ramanujan conjecture in this setting follows from Eichler--Shimura plus Deligne. Perhaps, the novel "non-geometric" case is when $F$ is imaginary and the cuspidal automorpic representation is "regular algebraic of weight 0" in the sense of the paper (analogous to the case of classical modular cusp forms, etc of weight $k=2$). | |
| Dec 28, 2018 at 5:17 | comment | added | Victor Protsak | Well, the correspodence with the original question is far from obvious. The setting of this paper, involving ${\rm GL}_n(F)$ and a related group $\widetilde{G}$ for an imaginary CM field $F$, is rather technical. But if I understand correctly, the "weight zero" condition for $n=2$ and $F$ totally real would correspond to Hilbert modular forms of weight 2 at the archimedean places. Ramanujan conjecture in this context asserts that all non-archimedean local components are tempered representations of the corresponding ${\rm GL}_2(F_v)$. | |
| Dec 27, 2018 at 23:58 | comment | added | student | @VictorProtsak, I did say <i>for a class of automorphic forms</i>. Did I say something misleading? I confess your comment has gone over my head. | |
| Dec 27, 2018 at 21:34 | comment | added | Victor Protsak | From the abstract, it appears that only weight zero case of the Ramanujan conjecture is treated. | |
| Dec 27, 2018 at 16:00 | review | Late answers | |||
| Dec 27, 2018 at 16:15 | |||||
| Dec 27, 2018 at 15:45 | review | First posts | |||
| Dec 27, 2018 at 19:08 | |||||
| Dec 27, 2018 at 15:40 | history | answered | student | CC BY-SA 4.0 |