|
Search: id:A138551
|
|
|
| A138551 |
|
Moment sequence of t^3 coefficient in det(tI-A) for random matrix A in USp(6). |
|
+0
2
|
|
| 1, 0, 2, 0, 23, 0, 684, 0, 34760, 0, 2493096, 0, 228253267, 0, 25091028820, 0, 3179942075960, 0, 451649016238160, 0, 70421753109861592, 0, 11869050034269797984, 0, 2136758627313217104448, 0
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Let the random variable X be the coefficient of t^3 in the characteristic polynomial det(tI-A) of a random matrix in USp(6) (6x6 complex matrices that are unitary and symplectic). Then a(n) = E[X^n].
Let L_p(T) be the L-polynomial (numerator of the zeta function) of a genus 3 curve C. Under a generalized Sato-Tate conjecture, for almost all C,
a(n) is the nth moment of the coefficient of t^3 in L_p(t/sqrt(p)), as p varies.
|
|
REFERENCES
|
Kiran S. Kedlaya and Andrew V. Sutherland, "Hyperelliptic curves, L-polynomials and random matrices", preprint, 2008.
|
|
FORMULA
|
See Prop. 12 of Kedlaya-Sutherland reference below.
|
|
EXAMPLE
|
a(4) = 23 because E[X^4] = 23 for X the t^3 coeff of det(tI-A) in USp(6).
|
|
CROSSREFS
|
Cf. 138540, 138549.
Sequence in context: A156438 A009378 A106708 this_sequence A133490 A051728 A005359
Adjacent sequences: A138548 A138549 A138550 this_sequence A138552 A138553 A138554
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Andrew V. Sutherland (drew(AT)math.mit.edu), Mar 24 2008
|
|
|
Search completed in 0.002 seconds
|
