Timeline for Sato-Tate measure for GL(3) Automorphic forms
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 6, 2014 at 14:32 | answer | added | David E Speyer | timeline score: 6 | |
| Dec 3, 2012 at 23:54 | vote | accept | 7-adic | ||
| Sep 1, 2012 at 17:52 | vote | accept | 7-adic | ||
| Dec 3, 2012 at 23:53 | |||||
| Jul 25, 2012 at 15:09 | vote | accept | 7-adic | ||
| Sep 1, 2012 at 17:52 | |||||
| Jul 8, 2012 at 22:33 | vote | accept | 7-adic | ||
| Jul 25, 2012 at 15:09 | |||||
| Jul 8, 2012 at 7:21 | history | edited | 7-adic | CC BY-SA 3.0 |
deleted 30 characters in body
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| Jul 8, 2012 at 5:59 | comment | added | Emerton | Correction: As Qiaochu notes below, a conjugacy class in SU(3) is determined by its trace, despite my claim to the contrary above. | |
| Jul 7, 2012 at 17:45 | answer | added | Qiaochu Yuan | timeline score: 7 | |
| Jul 7, 2012 at 16:47 | answer | added | David Hansen | timeline score: 12 | |
| Jul 7, 2012 at 16:33 | comment | added | Marty | You might want to see the closely related question I asked: mathoverflow.net/questions/25929/u3-sato-tate-measure My perspective now is that a closed form for the measure is messy, and it's better to compute moments instead. There are closed forms for the first few moments for the SU(3) Sato-Tate measure (I remember the number 12 since it agreed with my student's numerical evidence). | |
| Jul 7, 2012 at 15:35 | comment | added | Emerton | ... when $n = 2$. Regards, | |
| Jul 7, 2012 at 15:35 | comment | added | Emerton | ... a pushforward measure on $[-3,3]$ which will determine the distribution of traces. This is an exercise in Lie theory which I haven't done. If you work in a context where the determinant is not (say) a power of the cyclotomic character, then things become slightly more complicated (this corresponds, I think, to your remark about the possibility of imaginary eigenvalues), and the group $SU(n)$ has to be replaced with $U(n)$ (or perhaps some intermediate group). You can look at the recent paper of Barnet-Lamb--Gee--Geraghty on Sato--Tate for Hilbert modular forms to see how this goes ... | |
| Jul 7, 2012 at 15:29 | comment | added | Emerton | Dear 7-adic, Ignoring possible issues with determinants, Sato--Tate measure for $n$-dimensional Galois representations will be the pushforward of Haar measure on $SU(n)$ to the space of conjugacy classes in $SU(n)$. In the case of $SU(2)$, the space of conjugacy classes is naturally in bijection with $[-2,2]$ (by taking the trace), and Sato--Tate measure gets identified with the measure you indicated on that interval. In the case of $SU(3)$, trace does not suffice to determine a conjugacy class. Nevertheless, you could pushforward Sato--Tate measure under the trace map, to obtain ... | |
| Jul 7, 2012 at 15:14 | history | asked | 7-adic | CC BY-SA 3.0 |