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A138549
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Moment sequence of t^2 coefficient in det(tI-A) for random matrix A in USp(6).
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2
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1, 1, 2, 5, 16, 62, 282, 1459, 8375, 52323, 350676, 2493846, 18659787, 145918295, 1186129168, 9978055080, 86545684565, 771571356565, 7051538798490, 65913863945775, 628919704903746, 6114899366942556, 60492393411513722
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OFFSET
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0,3
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COMMENTS
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Let the random variable X be the coefficient of t^2 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 n-th moment of the coefficient of t^2 in L_p(t/sqrt(p)), as p varies.
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LINKS
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FORMULA
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See Prop. 12 of first Kedlaya-Sutherland reference.
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EXAMPLE
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a(3) = 5 because E[X^3] = 5 for X the t^2 coeff of det(tI-A) in USp(6).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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