Timeline for Are there cusp forms for the full modular group Sp(2,Z) and representations det^3 \otimes Sym^2j(\rho_standard)
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| May 23, 2014 at 8:28 | answer | added | Dan Petersen | timeline score: 2 | |
| Oct 12, 2013 at 12:33 | history | edited | Tom | CC BY-SA 3.0 |
corrected spelling of Tsushima
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| Jul 27, 2013 at 14:16 | comment | added | Tom | Just sent you a mail ! It's great that I get to know people by this question. | |
| Jul 27, 2013 at 13:32 | comment | added | Dan Petersen | Oh -- you're right! I was thinking of the fact that Conjecture 6.3 in B-F-VdG is open both for local systems of the form $\mathbb V_{a,0}$ and $\mathbb V_{a,a}$; the former correspond to SMFs with $k=3$ and the latter to ones with $j=0$. It is this conjecture I think I can prove for the ones of the form $\mathbb V_{a,0}$. But of course it's already known that Tsushima's formula holds for scalar valued SMFs. Anyway this is work in progress and there are still things to check, so if you are interested you can send me an e-mail. | |
| Jul 27, 2013 at 11:15 | comment | added | Tom | I'm puzzled now if you can give an ad hoc proof of the case $k=3, j\geq 0$ then you have proven the whole conjecture in a glimpse, haven't you ? | |
| Jul 27, 2013 at 10:55 | comment | added | Dan Petersen | Tsushima's dimension is conjectured to hold for any $k \geq 3$, $j \geq 0$. There is strong evidence for this conjecture coming from point counts of moduli spaces over finite fields, see Section 6 of Bergström, Faber, Van der Geer: Siegel modular forms of degree three adn the cohomology of local systems. If you are interested I think I might be able to give an ad hoc proof of the case $k=3$, $j \geq 0$. | |
| Jul 27, 2013 at 10:12 | vote | accept | Tom | ||
| Jul 27, 2013 at 10:11 | history | edited | Tom | CC BY-SA 3.0 |
added the articles by Ibukiyama, Satoh and van Dorp and highlighted Tshushima's article
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| Jul 19, 2012 at 2:48 | answer | added | ncr | timeline score: 4 | |
| Jul 18, 2012 at 20:11 | history | asked | Tom | CC BY-SA 3.0 |