For q ≡ 2 mod 3, it claims the second moment of primitive cubic L-functions of genus g is (g(g+2)/8) A_q(1/q^2, 1/q^{3/2}) ζ_q(3/2)^2 ζ_q(3)^{-1} q^{g+2} + O(q^g).
Theta functions on the n -fold metaplectic cover of SL (2) ---the function field case
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The second moment of cubic Dirichlet L-functions over function fields
For q ≡ 2 mod 3, it claims the second moment of primitive cubic L-functions of genus g is (g(g+2)/8) A_q(1/q^2, 1/q^{3/2}) ζ_q(3/2)^2 ζ_q(3)^{-1} q^{g+2} + O(q^g).