An asymptotic formula is computed for the moment of the product of spinor and standard L-functions of degree-two holomorphic Siegel cusp forms, with applications to joint non-vanishing and lower bounds on second moments.
Blomer, On the central value of symmetric square L -functions, Math
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Moments and joint nonvanishing of symplectic $L$-functions
An asymptotic formula is computed for the moment of the product of spinor and standard L-functions of degree-two holomorphic Siegel cusp forms, with applications to joint non-vanishing and lower bounds on second moments.