Timeline for The Langlands parameters of the symmetric cube lifts of cusp forms
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 21, 2022 at 1:55 | comment | added | hofnumber | @WindomEarle Great thanks also for your warm-hearted help, dear Windom Earle. | |
| Jul 21, 2022 at 1:53 | comment | added | hofnumber | @YemonChoi Great thanks for your kindly comments. | |
| Jul 18, 2022 at 18:25 | comment | added | Windom Earle | The computation can be carried out precisely as Prof. Loeffler described. This is essentially Linear Algebra. There is actually a very nice paper by Michel and Cogdell 'On the complex moments of the symmetric square L-function at s=1' where precisely this computation is carried out in great detail. (See section 3 of the paper: doi.org/10.1155/S1073792804132455 ). | |
| Jul 18, 2022 at 18:08 | comment | added | Yemon Choi | Dear @hofnumber - you say that you have seached many papers, and you have asked several questions on this site that seem quite specialized or technical, but it is unclear from your questions and comments what previous background you have. It is suprising that you say you are not familar with group representations, if you are asking questions about Langlands parameters or Maass forms. Perhaps it would be more productive if you asked more basic questions about the concepts involved? | |
| Jul 18, 2022 at 9:53 | comment | added | hofnumber | Dear Prof. Loeffler, I have, yes, searched many papers, however it seems that there is no any account on the associated parameters $\alpha_1,\alpha_2,\alpha_3,\alpha_4. $ And, to be frankly, I am not familiar with the group representations. It's maybe not an easy exercise to work out the Langlands parameter to any given $2\times 2 $ diagonal matrix, for which I really need some help from the top experts like you here. | |
| Jul 18, 2022 at 8:17 | comment | added | David Loeffler | You seem unwilling to put in any work yourself here. | |
| Jul 18, 2022 at 8:03 | comment | added | hofnumber | Dear Prof. Loeffler, thanks for explanation, definitely I was concerned about the Langlands parameters just from the point of view of the functional equation of the $L$-function of $L(s, \text{sym}^3f)$. Particularly, I need the exact forms of the Gamma factors of the $L$-function from the symmetric cube lifts of the $GL_2$-cusp forms. So, could you please give some more specific information on the associated parameters $\alpha_1,\alpha_2,\alpha_3,\alpha_4$? This is really what I am concerned about. Much obliged! | |
| Jul 18, 2022 at 7:43 | history | answered | David Loeffler | CC BY-SA 4.0 |