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Numerical computation of a certain Dirichlet series attached to Siegel modular forms of degree two

Authors: Nathan C. Ryan, Nils-Peter Skoruppa and Fredrik Strömberg
Journal: Math. Comp. 81 (2012), 2361-2376
MSC (2010): Primary 11F46, 11F66; Secondary 11F27, 11F50
Published electronically: February 20, 2012
MathSciNet review: 2945160
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Abstract: 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 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.

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Additional Information

Nathan C. Ryan
Affiliation: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837

Nils-Peter Skoruppa
Affiliation: Fachbereich Mathematik, Universität Siegen, Germany

Fredrik Strömberg
Affiliation: Fachbereich Mathematik, TU-Darmstadt, Germany

Received by editor(s): August 12, 2010
Received by editor(s) in revised form: June 7, 2011
Published electronically: February 20, 2012
Additional Notes: This project was supported by the National Science Foundation under FRG Grant No. DMS-0757627, the authors also made use of hardware provided by DMS-0821725.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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