Timeline for Does anyone want a pretty Maass form?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 6, 2010 at 1:38 | comment | added | Junkie | Yes, now I remember having someone else tell me the same thing about JRS and it not being totally real. Does not Jehanne carry out for totally real though? Viz. Examples 2-5 (page 353-6) for example has $x^5-17*x^3+30*x^2-4*x-7$ and three others of totally real type. A general purpose tool like SAGE/Magma is wrong for a special case, so the original poster would have the right idea to specialize the code. | |
| May 5, 2010 at 9:32 | comment | added | Kevin Buzzard | no! They only work with odd Galois representations, which are all known to be modular (by Khare-Wintenberger, although in fact the reps they work with were known to be modular earlier---see Remark 3.3). I should have been clearer: can you come up with a_p for a totally real A_5 extension? Then one can check to see if the Maass form looks like it exists and this is a computation that cannot be deduced from general theory. | |
| May 5, 2010 at 8:27 | comment | added | Junkie | Actually, Sands, Jehanne, Roblot cover this in section 3.4 of emis.de/journals/EM/expmath/volumes/12/12.4/Roblot.pdf explaining how to compute everything. They quote a paper of Jehanne for the coefficient calculation dx.doi.org/10.1006/jnth.2001.2656 They verify Stark's conjecture, so I guess everything works. | |
| May 5, 2010 at 7:57 | comment | added | Kevin Buzzard | Very nice. Can you do an A_5 example?? | |
| May 5, 2010 at 7:30 | history | answered | Junkie | CC BY-SA 2.5 |