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 A138551 Moment sequence of t^3 coefficient in det(tI-A) 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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 n-th moment of the coefficient of t^3 in L_p(t/sqrt(p)), as p varies. LINKS Table of n, a(n) for n=0..25. Kiran S. Kedlaya and Andrew V. Sutherland, Hyperelliptic curves, L-polynomials and random matrices, arXiv:0803.4462 [math.NT], 2008-2010. FORMULA See Prop. 12 of Kedlaya-Sutherland. EXAMPLE a(4) = 23 because E[X^4] = 23 for X the t^3 coeff of det(tI-A) in USp(6). CROSSREFS Cf. A138540, A138549. Sequence in context: A254042 A009378 A106708 * A133490 A051728 A201954 Adjacent sequences: A138548 A138549 A138550 * A138552 A138553 A138554 KEYWORD nonn AUTHOR Andrew V. Sutherland, Mar 24 2008 STATUS approved

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Last modified November 29 13:27 EST 2023. Contains 367445 sequences. (Running on oeis4.)