The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.
Mathematics of Computation
First published in Mathematics of Computation in Vol. 81, No. 280, Oct. 2012, published by the American Mathematical Society.
Ryan, Nathan C.; Skoruppa, Nils-Peter; and Stroemberg, Fredrik. "Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two." Mathematics of Computation (2012) : 2361-2376.