Timeline for U(3) Sato-Tate measure.
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 11, 2013 at 18:28 | comment | added | user30830 | So did you find the density of $Tr(g)=z$??? What is the formula? | |
| Sep 1, 2012 at 21:40 | comment | added | Marty | It's just Haar measure on U(3). | |
| Sep 1, 2012 at 18:05 | comment | added | 7-adic | Did you know who firstly introduced this measure? Was that Katz-Sarnak? | |
| Jun 2, 2010 at 18:14 | comment | added | Marty | Just an update -- computations are done and agree with predicted moments! The Rains paper, as well as earlier work of Diaconis-Shashahani was extremely helpful. | |
| May 27, 2010 at 23:43 | comment | added | Marty | Correct, generically. But I'm having the undergraduate work with "Picard curves" -- certain genus three curves whose Jacobian has extra endomorphisms (by the ring of integers in $Q(\sqrt{-3})$). These extra endomorphisms cut down the image of the Galois representation from $USp(6)$ to $U(3)$ (at primes congruent to $1$ mod $3$), and make it an interesting case to study. It's a natural first choice to study, if one wants to go beyond the $SU(2)$ regime. | |
| May 27, 2010 at 20:03 | comment | added | David Hansen | I thought that the roots of local L-functions of curves seemed to be drawn from USp(2g), not just a unitary group...? | |
| May 26, 2010 at 14:15 | comment | added | Marty | Thanks for the references! I hadn't found the Rains paper before, which sounds very promising. I'll take a look later today, but it sounds like exactly what I want. | |
| May 26, 2010 at 11:52 | comment | added | Junkie | I should have said all positive integers of course. The moments are given in Sloane as A005802. research.att.com/~njas/sequences/A005802 | |
| May 26, 2010 at 10:50 | answer | added | Charles Matthews | timeline score: 3 | |
| May 26, 2010 at 7:39 | comment | added | Junkie | I think that Rains (after Diaconis-Shashahani) found the expected value of $|Tr(U)|^{2k}$ for all integers k (not just those up to the dimension $N$), from which you can apply inversion, I guess? See: combinatorics.org/Volume_5/PDF/v5i1r12.pdf I got this from a paper of Tracy (see page 2), who notes work of Gessel. Tracy: arxiv.org/pdf/math.CO/9811154 Gessel: people.brandeis.edu/~gessel/homepage/papers/dfin.pdf Sorry, that's the best I can do for now. | |
| May 25, 2010 at 21:08 | history | edited | Marty | CC BY-SA 2.5 |
another dumb mistake.
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| May 25, 2010 at 20:37 | history | asked | Marty | CC BY-SA 2.5 |