

A138551


Moment sequence of t^3 coefficient in det(tIA) for random matrix A in USp(6).


1



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
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OFFSET

0,3


COMMENTS

Let the random variable X be the coefficient of t^3 in the characteristic polynomial det(tIA) 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 Lpolynomial (numerator of the zeta function) of a genus 3 curve C. Under a generalized SatoTate 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.


LINKS



FORMULA

See Prop. 12 of KedlayaSutherland.


EXAMPLE

a(4) = 23 because E[X^4] = 23 for X the t^3 coeff of det(tIA) in USp(6).


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



