Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

Details Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

2010-09-16

arxiv.org/abs/1009.3198v1

Mathematics

Number Theory

15 pages

Scientific paper

The Rankin convolution type Dirichlet series $D_{F,G}(s)$ 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 $D_{F,G}(s)$, which share 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.

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