|
Search: id:A138350
|
|
|
| A138350 |
|
Moment sequence of tr(A^2) in USp(4). |
|
+0
3
|
|
| 1, -1, 3, -6, 20, -50, 175, -490, 1764, -5292, 19404, -60984, 226512, -736164, 2760615, -9202050, 34763300, -118195220, 449141836, -1551580888, 5924217936, -20734762776, 79483257308, -281248448936, 1081724803600, -3863302870000, 14901311070000, -53644719852000
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
If A is a random matrix in the compact group USp(4) (4 X 4 complex matrices which are unitary and symplectic), then a(n)=E[(tr(A^2)^n] is the n-th moment of the trace of A^2. See A138351 for central moments.
|
|
REFERENCES
|
Kiran S. Kedlaya and Andrew V. Sutherland, "Hyperelliptic curves, L-polynomials and random matrices", preprint, 2008.
|
|
LINKS
|
Kiran S. Kedlaya and Andrew V. Sutherland, Hyperelliptic curves, L-polynomials and random matrices.
|
|
FORMULA
|
a(n)=(1/2)Integral_{x=0..Pi,y=0..Pi}(2cos(2x)+2cos(2y))^n(2cos(x)-2cos(y))^2(2/Pi*sin^2(x))(2/Pi*sin^2(y))dxdy. a(n)=A126120(n)A138364(n+1)-A138364(n)A126120(n+1)
|
|
EXAMPLE
|
a(5) = -50 because E[(tr(A^2))^5] = -50 for a random matrix A in USp(4).
a(5) = A126120(5)A138364(6)-A138364(5)A126120(6) = 0*0-10*5 = -50
|
|
CROSSREFS
|
A signed version of A005558, which is the main entry for this sequence. Cf. A138349, A138351.
Sequence in context: A148573 A148574 A005558 this_sequence A148575 A148576 A148577
Adjacent sequences: A138347 A138348 A138349 this_sequence A138351 A138352 A138353
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Andrew V. Sutherland (drew(AT)math.mit.edu), Mar 16 2008
|
|
|
Search completed in 0.002 seconds
|
