Multiple Dirichlet series heuristics reproduce, and for elliptic curve twists correct, the standard moment predictions for four families of L-functions, with each recipe term matched to a residue.
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Multiple Dirichlet series predictions for moments of $L$-functions: unitary, symplectic and orthogonal examples
Multiple Dirichlet series heuristics reproduce, and for elliptic curve twists correct, the standard moment predictions for four families of L-functions, with each recipe term matched to a residue.